% \iffalse meta-comment
%
% Copyright (C) 2005-2011 by David Zaslavsky <diazona@ellipsix.net>
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3 or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status `maintained'.
%
% The Current Maintainer of this work is David Zaslavsky
%
% This work consists of the files physymb.dtx and physymb.ins
% and the derived files physymb.sty and physymb.pdf.
%
% \fi

% \iffalse
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%<package>\ProvidesPackage{physymb}[2010/12/15 v0.1 Physics symbol definitions]
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\documentclass{ltxdoc}
\usepackage[boldvectors,units]{physymb}
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%% \CharacterTable
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%%   Exclamation   \!     Double quote  \"     Hash (number) \#
%%   Dollar        \$     Percent       \%     Ampersand     \&
%%   Acute accent  \'     Left paren    \(     Right paren   \)
%%   Asterisk      \*     Plus          \+     Comma         \,
%%   Minus         \-     Point         \.     Solidus       \/
%%   Colon         \:     Semicolon     \;     Less than     \<
%%   Equals        \=     Greater than  \>     Question mark \?
%%   Commercial at \@     Left bracket  \[     Backslash     \\
%%   Right bracket \]     Circumflex    \^     Underscore    \_
%%   Grave accent  \`     Left brace    \{     Vertical bar  \|
%%   Right brace   \}     Tilde         \~}
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% \GetFileInfo{physymb.sty}
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% \DoNotIndex{\accentset,\addunit,\allowdisplaybreaks}
% \DoNotIndex{\bar,\boolean}
% \DoNotIndex{\cos,\cubic}
% \DoNotIndex{\dagger,\DeclareFontShape,\DeclareMathAlphabet,\DeclareMathOperator}
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%
% \title{The \textsf{physymb} package\thanks{This document corresponds to \textsf{physymb}~\fileversion, dated~\filedate.}}
% \author{David Zaslavsky \\ \texttt{diazona@ellipsix.net}}
%
% \maketitle
% \begin{abstract}
%  The |physymb| package is nothing but a bunch of simple macro definitions that
%  may be useful for typesetting physics papers.
% \end{abstract}
%
% \paragraph{What's so great about it?}
% If you're scanning over this document wondering what good a bunch of simple macro
% definitions are, allow me to point out some highlights:
% \begin{itemize}
%  \item Total and partial derivatives can be typeset using two character macros.\\
%   $\ud{y}{x}$ is now as easy as |\ud{y}{x}|.
%  \item Numbers in scientific notation can also be typeset using a two character macro.
%   $\sn{6.23}{6}$ is written |\sn{6.23}{6}|.
%  \item Doing the same thing with units added is similarly convenient; you can write
%   $\snunit{3.1}{6}{\meter^3}$ as |\snunit{3.1}{6}{\meter^3}|, which is a lot more
%   convenient than writing the whole thing out ``manually.''
%  \item There are standard, simple macros for writing Dirac notation: $\ket{\psi}$ is
%   as easy as |\ket{\psi}|.
% \end{itemize}
%
% There are a lot of macros in this package, and it typically doesn't take as many
% lines to explain their meanings as it does to list them all. For that reason, when
% there are a bunch of similar macros that I explain together, I've usually only listed
% one or two in the left margin. In these cases, all the macros are given in the text.
%
% \section{Options}
%
% |physymb| recognizes the following options, in no particular order.
%
% \begin{itemize}
%  \item |arrowvectors| causes vectors (specifically, the |\vec| command) to be rendered
%   with an arrow above the symbol.
%  \item |boldvectors| causes vectors (again, from |\vec|) to be rendered by typesetting
%   the symbol in bold. It's the alternative to |arrowvectors|.
%  \item |feynman| pulls in the |feynmp| package. (It's precisely equivalent to
%   |\usepackage{feynmp}|, it's just here for convenience.)
%  \item |particle| enables all the particle physics macros. (It's actually not implemented
%   yet, so in practice the particle macros get defined regardless of whether you pass this
%   option or not, but that will be fixed soon.)
%  \item |units| pulls in the |SIunits| package and enables the additional unit macros.
% \end{itemize}
%
% \section{Macros}
%
% \subsection{Trigonometry}
%
% \DescribeMacro{\asin}
% \DescribeMacro{\acos}
% The AMS packages only define inverse trigonometric functions using the ``arc''
% syntax, i.e. they actually prefix ``arc'' to the name (as in $\arcsin x$).
% Sometimes you'd rather write them with a superscript $-1$ to save space, so
% those versions are included here. We have the inverse functions |\asin|,
% |\acos|, |\atan|, |\asec|, |\acsc|, and |\acot|.
%
% \DescribeMacro{\sech}
% \DescribeMacro{\cosh}
% For some reason, the hyperbolic sine and cosine |\sech| and |\cosh| aren't
% defined in the AMS packages. This fixes that.
%
% \DescribeMacro{\asinh}
% \DescribeMacro{\acosh}
% Finally, the inverse hyperbolic trig functions written with the superscript
% $-1$ are defined just as with the regular inverse trig functions. We have
% |\asinh|, |\acosh|, |\atanh|, |\asech|, |\acsch|, and |\acoth|.
%
% \subsection{Sets}
%
% There are certain sets of numbers that are semi-frequently referenced in physics.
% Typically they're used to say something like $n\in\intset$. Of course, a
% macro like |\intset| is not necessarily much quicker than writing
% |\mathbb{Z}|, but these macros are intended to have names that relate to
% their meanings so that you don't have to remember which letter goes to which set.
%
% \DescribeMacro{\whlset}
% |\whlset| ($\whlset$) denotes the set of whole numbers, which is typically
% defined to include all integers greater than zero, although there are different
% contradictory definitions floating around.
%
% \DescribeMacro{\natset}
% |\natset| ($\natset$) denotes the set of natural numbers, which is typically
% defined to include all integers greater than or equal to zero. Some people
% define ``natural numbers'' to exclude zero.
%
% \DescribeMacro{\intset}
% |\intset| ($\intset$) denotes the set of all integers.
%
% \DescribeMacro{\realset}
% |\realset| ($\realset$) denotes the set of all real numbers.
%
% \DescribeMacro{\imagset}
% |\imagset| ($\imagset$) denotes the set of all imaginary numbers, which is
% all complex numbers with real part equal to zero. This one is infrequently
% used.
%
% \DescribeMacro{\cpxset}
% |\cpxset| ($\cpxset$) denotes the set of all complex numbers.
%
% \subsection{Calculus}
%
% Probably the most useful macros in the package are the derivative operators.
% Since it's so common to write something of the form $\ud{y}{x}$ or $\pd{y}{x}$,
% we have two-character macros for each:
% \begin{itemize}
%  \item \DescribeMacro{\ud} |\ud|\marg{top}\marg{bottom} typesets the normal total derivative
%  \item \DescribeMacro{\pd} |\pd|\marg{top}\marg{bottom} typesets a partial derivative, which
%   is the same thing but with a partial derivative symbol instead of the $\udc$.
% \end{itemize}
% \DescribeMacro{\udd}
% \DescribeMacro{\uddd}
% \DescribeMacro{\pdd}
% \DescribeMacro{\pddd}
% There are variants of these that produce higher-order derivatives; you can add
% an order by adding another |d|, up to a total of three.
% If you need something higher than the third derivative, you're on your own, but it's
% easy to construct it using |\frac| and |\udc| or |\pdc|,
% \begin{center}
%  |\frac{\udc^4 y}{\udc x^4}|
% \end{center}
%
% \DescribeMacro{\udc}
% \DescribeMacro{\pdc}
% The macro |\udc| gives you the character that represents a differential. It's typically
% set in roman type to distinguish it from a variable. |\pdc| is also defined as the
% partial derivative character for consistency. There are variants of each with exponents
% (up to 3) built in; again, you get them by adding an extra |d| or two to the name of the
% command, |\uddc| and |\udddc| and so on.
%
% \DescribeMacro{\uds}
% \DescribeMacro{\pds}
% If you're using these in an integral, it's common to want a small space before the
% differential, so there are variants of the preceding commands defined that include
% this small space for you; they replace the |c| with an |s|. They follow the same
% pattern of adding additional |d|'s to get exponents. For example:
%
% \begin{minipage}{.64\textwidth}
% \begin{center}
%  |\iint e^{i\vec{k}\cdot\vec{x}}\udds\vec{x}|
% \end{center}
% \end{minipage}
% \begin{minipage}{.34\textwidth}
% \begin{equation*}
%  \iint e^{i\vec{k}\cdot\vec{x}}\udds\vec{x}
% \end{equation*}
% \end{minipage}
%
% \subsection{Vector Calculus}
%
% \DescribeMacro{\div}
% \DescribeMacro{\grad}
% \DescribeMacro{\curl}
% |\physymb| defines |\div|, |\grad|, and |\curl|, to represent the
% divergence, gradient, and curl. These are typeset with the nabla
% (or ``del'') character, $\nabla$, rather than being written out
% as words. Naturally, I would love to add an |\allthat| if I can
% find something good for it to represent.
%
% \DescribeMacro{\lapl}
% There is also a macro for the Laplacian operator (divergence of a
% gradient), |\lapl|.
%
% \subsection{Complex Analysis}
%
% \DescribeMacro{\conj}
% There is a macro to indicate the conjugate of a number, |\conj|\marg{number}.
% It puts a superscript star after the number, as in $\conj{z}$.
%
% \DescribeMacro{\realop}
% \DescribeMacro{\imagop}
% The traditional keywords indicating the real and imaginary parts of a complex number
% are given macros |\realop| and |\imagop|. They typeset $\realop$ and $\imagop$
% respectively.
%
% \DescribeMacro{\real}
% \DescribeMacro{\imag}
% Why the |op|? Well, there are alternate versions that will also put curly braces
% around the following argument, |\real| and |\imag|. This is the way $\realop$ and
% $\imagop$ are often used.
%
% \begin{minipage}{.64\textwidth}
% \begin{center}
%  |\real{z}, \imag{z}|
% \end{center}
% \end{minipage}
% \begin{minipage}{.34\textwidth}
% \begin{equation*}
%  \real{z}, \imag{z}
% \end{equation*}
% \end{minipage}
%
% \DescribeMacro{\abs}
% The macro |\abs|\marg{value} surrounds its argument with vertical bars.
%
% \subsection{Linear Algebra}
%
% There are several assorted macros for linear algebra keywords and concepts.
%
% \DescribeMacro{\vec}
% \DescribeMacro{\vecvar}
% Vectors can be written using the macro |\vec|\marg{label}, which typesets
% the \meta{label} either in bold or with an arrow over it, according to which
% option was passed to the package (|arrowvectors| or |boldvectors|).
% The default is to use an arrow, to resemble the builtin definition of
% |\vec| (which, by the way, is overridden by this package). In many cases
% I prefer bold. |\vecvar|\marg{label} is another macro that does the exact
% same thing, for consistency with the other kinds of variables.
%
% \DescribeMacro{\tnsvar}
% The macro |\tnsvar|\marg{label} is for typesetting tensors. This just makes
% the \meta{label} bold, it doesn't do anything with indices. If you want a way
% to typeset tensor indices, look at the
% \href{http://tug.ctan.org/cgi-bin/ctanPackageInformation.py?id=tensor}{tensor}
% package.
%
% \DescribeMacro{\matvar}
% |\matvar|\marg{label} is intended to designate matrices. It makes the label
% bold.
%
% \DescribeMacro{\identitym}
% The macro |\identitym| represents the identity matrix. It typesets a 1 in
% the same style as |\matvar| (so, bold).
%
% \DescribeMacro{\determinant}
% The macro |\determinant|\marg{matrix} uses vertical bars to denote the determinant
% of the \meta{matrix}. It's an alternative to the keyword operator |\det|, which
% just typesets as $\det$.
%
% \DescribeMacro{\trace}
% The macro |\trace| just typesets $\trace$. It's akin to |\det|.
%
% \DescribeMacro{\diag}
% This just typesets $\diag$, which is used to represent a matrix with the given entries
% on the diagonal. For example, one might write |\diag(1,2,3,4)|.
%
% \DescribeMacro{\norm}
% The norm of a vector can be denoted by double vertical bars. This is implemented by
% |\norm|\marg{value}.
%
% \DescribeMacro{\unitx}
% \DescribeMacro{\unity}
% \DescribeMacro{\unitz}
% Since it's so common to refer to unit vectors using hat notation, there are a
% bunch of macros for them using various letters. The package defines |\unitd|,
% |\unite|, |\uniti|, |\unitj|, |\unitk|, |\unitl| (which typesets as $\unitl$,
% not the normal $l$), |\unitn|, |\unitp|, |\unitq|, |\unitr|, |\units|, |\unitt|,
% |\unitu|, |\unitv|, |\unitw|, |\unitx|, |\unity|, |\unitz|, and for non-roman
% characters, |\unitphi|, |\unitrho|, |\unittheta|, and |\unitomega|.
% \DescribeMacro{\unitvec}
% If you want to use a different letter as a unit vector, it can be done with
% |\unitvec|\marg{symbol}.
%
% \DescribeMacro{\herm}
% |\herm|\marg{operator} designates the hermitian conjugate of an operator with
% a superscript dagger.
%
% \DescribeMacro{\transpose}
% |\transpose|\marg{matrix} sets a superscript $T$ after the matrix to denote
% the transpose.
%
% \DescribeMacro{\commut}
% \DescribeMacro{\acommut}
% There are simple macros for the commutator, |\commut|\marg{operator}\marg{operator},
% and the anticommutator, |\acommut|\marg{operator}\marg{operator}. They just
% put the appropriate kind of braces around the arguments (and the comma between
% them, of course).
%
% \subsection{Differential Geometry}
% \DescribeMacro{\exd}
% The exterior derivative has a macro, |\exd|, kind of like the macro for differentials
% ($\udc$) although typeset in bold to distinguish it. This one doesn't have any variants,
% though, because $\exd^2 = 0$.
%
% \DescribeMacro{\hodge}
% The macro |\hodge| just puts a star (not superscript) to represent the Hodge dual.
% Use it as a prefix to the variable, $\hodge\exd x$.
%
% \subsection{Classical Mechanics}
%
% \DescribeMacro{\pbrac}
% The Poisson brackets of a pair of variables can be typeset using the macro
% |\pbrac|\marg{function}\marg{function}. This just surrounds the two arguments
% with curly braces, producing $\pbrac{f}{g}$.
%
% \DescribeMacro{\pbracvars}
% If you want to specify which variables the derivatives in the Poisson brackets
% are being taken with respect to, use the variant
% \begin{center}
%  |\pbracvars|\marg{function}\marg{function}\marg{variable}\marg{variable}
% \end{center}
% It comes out looking like $\pbracvars{f}{g}{q}{p}$.
%
% \subsection{Quantum Mechanics}
%
% |physymb| includes a full set of macros for working with Dirac notation.
%
% \DescribeMacro{\ket} To typeset a ket ($\ket\psi$), use |\ket|\marg{label}.
% \DescribeMacro{\bra} Similarly, you can get a bra ($\bra\psi$), with |\bra|\marg{label}.
% \DescribeMacro{\braket} To typeset a bracket (inner product), use
% |\braket|\marg{bra label}\marg{ket label}.
%
% \DescribeMacro{\melement} To typeset a matrix element ($\melement{\phi}{A}{\psi}$), or any
% case in which you have an operator between the bra and the ket, use
% |\melement|\marg{bra label}\marg{operator}\marg{ket label}.
% It should work fine to put an arbitrarily complicated expression in the middle of |\melement|,
% but if your operator is something complicated, you \emph{could} consider just using |\bra|
% and |\ket| for clarity,
% \begin{center}
%  |\bra{|\meta{bra label}|}|\meta{operator}|\ket{|\meta{ket label}|}|
% \end{center}
%
% \DescribeMacro{\expect} To get an expectation value (an on-diagonal matrix element with
% the state left implicit, $\expect{A}$), use |\expect|\marg{operator}. Again, you can put
% an arbitrary expression within |\expect| but if it would make the code unclear, consider
% using |\langle| and |\rangle|.
%
% \DescribeMacro{\projop} For a projection operator (outer product between a state and itself),
% we have the command |\projop|\marg{label}\marg{value}, which comes out as $\projop{\psi}{x}$.
% To get a general outer product between two different states, use |\bra| and |\ket|,
% \begin{center}
%  |\ket{|\meta{ket label}|}|\meta{value}|\bra{|\meta{bra label}|}|
% \end{center}
%
% \subsection{Units}
%
% If the |units| option is provided to |physymb|, it automatically includes the |SIunits|
% package and defines some additional units that are often useful in practice.
%
% \DescribeMacro{\snunit} |\snunit|\marg{abcissa}\marg{exponent}\marg{unit} combines
% the functionality of |\sn| and |\unit|: it typesets a number in scientific notation
% with a following unit. If the abcissa is equal to $1$, it is omitted, so that
% |\snunit{1}{6}{\meter}| gives you $\snunit{1}{6}{\meter}$.
%
% \paragraph{SI units}
% \DescribeMacro{\joulepercubicmeter}
% \DescribeMacro{\joulepercubicmeterrp}
% These units of energy density have been useful to me approximately twice.
% Naturally, I had to include them. These augment the list of
% composite units made available by |SIunits| itself.
%
% \paragraph{Additional units} The |SIunits| package only includes SI units (as
% the name would suggest), but there are certain non-SI units that turn out to
% be occasionally useful when dealing with American non-scientists. |physymb|
% defines a selection of them as macros.
%
% \DescribeMacro{\torr}
% \DescribeMacro{\mmHg}
% Torr, |\torr|, and millimeters of mercury, |\mmHg|, are common atmospheric pressure units.
%
% \DescribeMacro{\amu}
% |\amu| represents the atomic mass unit, defined as $\frac{1}{12}$ of the mass of a carbon 12
% atom.
%
% \DescribeMacro{\yr}
% |\yr| represents a year with the symbol $\yr$. There are various definitions of
% different kinds of years floating around, but generally the symbol is the same.
%
% \DescribeMacro{\erg}
% |\erg| represents an erg, the CGS unit of energy, which still finds occasional use.
% Its value is $\snunit{1}{-7}{\joule}$.
%
% \DescribeMacro{\gauss}
% |\gauss| is the Gauss, a unit of magnetic field equal to $\snunit{1}{-4}{\tesla}$.
%
% \DescribeMacro{\molar}
% |\molar| represents a molar, a unit of concentration equal to one mole per liter.
% Strictly speaking, this is a chemistry unit, but it occasionally comes up in
% physics so it shouldn't hurt to have the macro around.
%
% \DescribeMacro{\poise}
% The poise is the CGS unit of viscosity, equal to $\unit{0.1}{\pascal\usk\second}$.
%
% \DescribeMacro{\foot}
% The foot is the Imperial unit of length, equal to $\unit{30.48}{\centi\meter}$.
%
% \DescribeMacro{\mileperhour}
% This is typically (or perhaps almost exclusively) used to measure transportation
% speeds: cars, trains, airplanes, etc. It's equal to about
% $\unit{0.447}{\frac{\meter}{\second}}$.
%
% \DescribeMacro{\pound}
% The pound is the Imperial unit of either force or mass, depending on who you
% ask. Technically I believe it is a force, but in many situations
% I've often found it clearer to treat it as a unit of mass and use $\mathrm{lbf}$
% (pound of force) as the unit of force. In this sense, it's equal to about
% $\unit{453.59}{\gram}$, and the pound of force is the weight of that mass
% under standard Earth surface gravity, which works out to about
% $\unit{4.448}{\newton}$.
%
% \subsection{Particle Physics}
%
% As a particle physicist, I do a lot of work that involves notation for elementary particles,
% so it's become useful to have a set of macros that produce standard written representations
% for them.\footnote{If there are other areas of physics in which a lot of short macros like
% these would be useful, I'm open to suggestions for adding them.} The names of the commands
% are pretty cryptic, but I've found that once you get used to using them, the names aren't
% hard to remember and the effort saved by having short macro names at least \emph{feels}
% worthwhile.
%
% In general, all the macro names follow the same pattern. Each one ends with a type
% code that identifies the type of particle: |q| for quark, |lp| for a ``regular'' lepton,
% |nu| for a neutrino, |br| for a baryon, |m| for a meson, and |bsn| for a boson. At the
% beginning is a particle code consisting of one or two letters that identify the specific
% particle within that type.
%
% Most of the basic macros consist of just those two parts. Antifermion macros are
% constructed by prepending an |a| to the type code. For vector bosons that occur in
% charge triplets, you prepend one of |p| (plus), |z| (zero), or |m| (minus) to indicate
% which one of the triplet you want. The same goes for baryons which occur in ``triplets''
% with the same name (three particles denoted by the same letter, even though they
% may not actually be a triplet). Singlet baryons have the |z| as well for consistency.
%
% The proton and neutron are named differently because their names are so common.
%
% \paragraph{Quarks}
% \DescribeMacro{\upq}
% \DescribeMacro{\dnq}
% Each of the quark macros is named with three letters. The first two letters are the
% particle code representing the name of the quark, and the third is the type code |q|.
% The macros are |\upq|, |\dnq|, |\srq|, |\chq|, |\btq|, and |\tpq|, representing the
% up, down, strange, charm, bottom, and top quarks, respectively.
%
% \DescribeMacro{\upaq}
% \DescribeMacro{\dnaq}
% The corresponding macros for the antiquarks are obtained by prepending |a| to the
% type code |q|. We have |\upaq|, |\dnaq|, |\sraq|, |\chaq|, |\btaq|, and |\tpaq|.
%
% \paragraph{Leptons}
% \DescribeMacro{\elp}
% \DescribeMacro{\enu}
% Leptons are done a little differently because there are two distinct types. The macros for
% the electron, muon, and tau lepton are named with a letter and |lp|: we have |\elp| for the
% electron, |\ulp| for the muon, and |\tlp| for the tau. Neutrino macros are constructed
% using the same first letter, but |nu| instead of |lp|: |\enu|, |\unu|, and |\tnu|.
%
% \DescribeMacro{\ealp}
% \DescribeMacro{\eanu}
% Antileptons are named with an |a| between the particle code and the type code.
% So we get |\ealp|, |\ualp|, and |\talp| for the ``regular'' antileptons and
% |\eanu|, |\uanu|, and |\tanu| for the antineutrinos.
%
% \paragraph{Baryons}
% \DescribeMacro{\lmzbr}
% \DescribeMacro{\sgpbr}
% \DescribeMacro{\sgzbr}
% \DescribeMacro{\sgmbr}
% Many of the most commonly referenced baryons in the standard model have
% macros defined. Each of these ends with the type code |br|. Most of them are built
% by putting a particle code and a charge letter together: we have |\lmzbr| for the
% lambda baryon; |\sgpbr|, |\sgzbr|, |\sgmbr| for the sigmas, |\xizbr| and |\ximbr|
% for the xi particles, and |\ommbr| for the omega of charge $-1$. The delta macros
% are named on the same principle but since there are four of them, we use two charge
% letters to indicate the $+2$ charge: |\dlppbr|, |\dlpbr|, |\dlzbr|, and |\dlmbr|.
%
% \DescribeMacro{\sgspbr}
% \DescribeMacro{\sgszbr}
% \DescribeMacro{\sgsmbr}
% In addition, there are macros for the starred (excited) versions of the sigmas and
% xis (only), obtained by adding an |s| before the charge letter: |\sgspbr| etc. and
% |\xiszbr| etc.
%
% \DescribeMacro{\prbr}
% \DescribeMacro{\nebr}
% The proton and neutron don't quite fall into the pattern because their names aren't
% used for multiple particles. The proton is |\prbr| and the neutron is |\nebr|.
%
% \DescribeMacro{\dlmmabr}
% The antiparticles to all these are obtained in \emph{almost} the usual way, by
% adding |a| just before the type code |br|. The one difference is that the charge
% letters are updated to reflect the actual charge of the antiparticle, so for example
% the antipartcle of the $\dlppbr$ (|\dlppbr|), the $\dlmmabr$, is written |\dlmmabr|,
% with two |m|'s because of its double-minus charge.
%
% \paragraph{Mesons}
% \DescribeMacro{\pipm}
% \DescribeMacro{\pizm}
% \DescribeMacro{\pimm}
% Essentially all the mesons defined in the standard model have macros. The naming can
% be a bit tricky because some of them are named as charge triplets while others are
% named as antiparticles. In the former case, we have the $\pi$s, |\pipm|, |\pizm|, and |\pimm|,
% and the $\rho$s, |\ropm|, |\rozm|, and |\romm|. (I'm not sure if it'd make it cleaner
% to just add the |h| into the names) The kaons have similar names, |\kapm|,
% |\kazm|, and |\kamm|, but there is also the $\kazam$, |\kazam|. Finally, the neutral
% mesons are named |\etam|, |\etapm| (here the |p| is for ``prime,'' not ``plus''), and
% |\phim|.
%
% \paragraph{Bosons}
% \DescribeMacro{\phbsn}
% \DescribeMacro{\Wpbsn}
% \DescribeMacro{\Wmbsn}
% There aren't that many bosons so the naming is simple: |\phbsn| for the photon,
% |\Zzbsn| for the neutral $\Zzbsn$, and |\Wpbsn| and |\Wmbsn| for the $\Wbsn$s. There's
% also |\Wbsn|, which does not indicate either charge, for when you need to refer to
% a generic $\Wbsn$ boson. The Higgs boson is written |\hbsn|.
%
% \DescribeMacro{\photon}
% Also, there is a macro |\photon| which is defined to be the same thing as |\phbsn|.
% It's included to support some old LaTeX files I wrote and although it will
% \emph{probably} not be removed from the package in the future, I make no guarantees.
%
% \subsection{Miscellaneous}
%
% \DescribeMacro{\sn} |\sn|\marg{abcissa}\marg{exponent} is a shorthand for setting a number
% in scientific notation. It works just like |\snunit| except that it does not take any unit
% as an argument.
%
% \DescribeMacro{\scriptr} |\scriptr| produces the script r found in Griffiths'
% electromagnetism textbook, or at least the closest equivalent in LaTeX, $\scriptr$.
%
% \DescribeMacro{\orderof} |\orderof|\marg{expression} represents the order of an
% expression, for example the error term in a perturbation series. Typical usage
% would be like
%
% \begin{minipage}{.64\textwidth}
% \begin{center}
%  |\frac{1}{1 - x} = 1 + x + \orderof{x^2}|
% \end{center}
% \end{minipage}
% \begin{minipage}{.34\textwidth}
% \begin{equation*}
%  \frac{1}{1 - x} = 1 + x + \orderof{x^2}
% \end{equation*}
% \end{minipage}
%
% It can also be used to discuss the growth of a function, e.g.
% ``$\orderof{x^3}$ for large $x$,'' or for similar uses such as big-O notation
% in computer algorithm analysis.
%
% \DescribeMacro{\sgn}
% There is a macro for the sign operator, |\sgn|, defined as
% \begin{equation*}
%  \sgn x = \begin{cases}1 & x > 0 \\ 0 & x = 0 \\ -1 & x < 0\end{cases}
% \end{equation*}
% (and yes, this is not really \emph{complex} analysis)
%
% \DescribeMacro{\round}
% Occasionally it's useful to have some way to designate rounding a number.
% The |\round| macro can be used for that. It comes out as $\round(x)$ (I do
% recommend the parentheses).
%
% \DescribeMacro{\evalat}
% The macro
% |\evalat|\marg{expression}\marg{lower limit}\marg{upper limit}
% is mainly useful for when you want to denote the numerical value
% of a derivative at a specific point, or when you want to represent the
% evaluation of an integral at the endpoints of the range of integration.
% It produces a vertical bar at the right of the \meta{expression},
% with the \meta{lower limit} and \meta{upper limit} typeset at the
% lower and upper endpoints of the bar, respectively.
%
% \begin{minipage}{.64\textwidth}
% \begin{center}
%  |\evalat{x^3 + 3x - 5}{2}{7}|
% \end{center}
% \end{minipage}
% \begin{minipage}{.34\textwidth}
% \begin{equation*}
%  \evalat{x^3 + 3x - 5}{2}{7}
% \end{equation*}
% \end{minipage}
%
% \StopEventually{\PrintChanges\PrintIndex}
%
% \section{Feedback}
%
% This package is always a work in progress, both in terms of adding new macros
% to the collection and fixing any errors or inconveniences in the ones that
% are already here. Any feedback you may have will be welcome at my email address,
% given at the top of the document.
%
% \section{Implementation}
%
% \subsection{Initialization}
%    \begin{macrocode}
\RequirePackage{ifthen}
%    \end{macrocode}
% This flag is set if the |particle| option is enabled. It enables definitions of particle symbol macros.
%    \begin{macrocode}
\newboolean{pparticle}
%    \end{macrocode}
% This flag is set if the |feynman| option is enabled. It pulls in the |feynmf| package.
%    \begin{macrocode}
\newboolean{pfeynman}
%    \end{macrocode}
% This flag is set if the |units| option is enabled. It pulls in the |SIunits| package and provides additional unit definitions.
%    \begin{macrocode}
\newboolean{punits}
%    \end{macrocode}
% This flag is set if the |boldvectors| option is enabled. It causes vectors to be rendered using a bold font instead of an overset arrow.
%    \begin{macrocode}
\newboolean{pboldvectors}
%    \end{macrocode}
%
% \subsection{Option Declarations}
% These are the option declarations, pretty self-explanatory.
%    \begin{macrocode}
\DeclareOption{particle}{\setboolean{pparticle}{true}}
\DeclareOption{units}{\setboolean{punits}{true}}
\DeclareOption{feynman}{\setboolean{pfeynman}{true}}
\DeclareOption{arrowvectors}{\setboolean{pboldvectors}{false}}
\DeclareOption{boldvectors}{\setboolean{pboldvectors}{true}}
\ProcessOptions\relax
%    \end{macrocode}
%
% \subsection{Macro Definitions}
% Here we bring in the AMS packages for mathematical notation.
%    \begin{macrocode}
\RequirePackage{amsbsy}
\RequirePackage{amsmath}
\RequirePackage{amsfonts}
\RequirePackage{amssymb}
\allowdisplaybreaks[2]
\RequirePackage{accents}
%    \end{macrocode}
% |calligra| is the package that includes the script r, $\scriptr$.
%    \begin{macrocode}
\RequirePackage{calligra}
\DeclareMathAlphabet{\mathcalligra}{T1}{calligra}{m}{n}
\DeclareFontShape{T1}{calligra}{m}{n}{<->s*[2.2]callig15}{}
\newcommand{\scriptr}{\mathcalligra{r}}
%    \end{macrocode}
% Scientific notation is implemented in the obvious way.
%    \begin{macrocode}
\newcommand{\sn}[2]{\ensuremath{#1\times10^{#2}}}
%    \end{macrocode}
% Here we load SIunits if the |units| option was passed.
%    \begin{macrocode}
\ifthenelse{\boolean{punits}}
{
 \RequirePackage[thinspace,mediumqspace,Gray,squaren]{SIunits}
%    \end{macrocode}
% These are some SI derived units that have been useful on occasion
%    \begin{macrocode}
 \addunit{\joulepercubicmeter}{\joule\per\cubic\meter}
 \addunit{\joulepercubicmeterrp}{\joule\usk\rpcubic\meter}
%    \end{macrocode}
% These are some useful non-SI units, defined using the SIunits internal command |\addunits|
%    \begin{macrocode}
 \addunit{\torr}{torr}
 \addunit{\mmhg}{mmHg}
 \addunit{\amu}{amu}
 \addunit{\yr}{yr}
 \addunit{\erg}{erg}
 \addunit{\gauss}{Ga}
 \addunit{\molar}{M}
 \addunit{\poise}{P}
 \addunit{\foot}{ft}
 \addunit{\mileperhour}{mph}
 \addunit{\pound}{lb}
%    \end{macrocode}
% |\snunit| is implemented using a combination of |\sn| and |\unit|
%    \begin{macrocode}
 \newcommand{\snunit}[3]{\ifthenelse{\equal{#1}{1}}%
  {\unit{10^{#2}}{#3}}{\unit{\sn{#1}{#2}}{#3}}}
}
{}
%    \end{macrocode}
% |\orderof| uses the calligraphic capital O, $\mathcal{O}$
%    \begin{macrocode}
\newcommand{\orderof}[1]{\ensuremath{\mathcal{O}\left(#1\right)}}
%    \end{macrocode}
% Now we come to assorted functions and keywords. First some inverse trig functions:
%    \begin{macrocode}
\DeclareMathOperator{\asin}{\sin^{-1}}
\DeclareMathOperator{\acos}{\cos^{-1}}
\DeclareMathOperator{\atan}{\tan^{-1}}
\DeclareMathOperator{\asec}{\sec^{-1}}
\DeclareMathOperator{\acsc}{\csc^{-1}}
\DeclareMathOperator{\acot}{\cot^{-1}}
%    \end{macrocode}
% and hyperbolic trig functions:
%    \begin{macrocode}
\DeclareMathOperator{\sech}{sech}
\DeclareMathOperator{\csch}{csch}
\DeclareMathOperator{\asinh}{\sinh^{-1}}
\DeclareMathOperator{\acosh}{\cosh^{-1}}
\DeclareMathOperator{\atanh}{\tanh^{-1}}
\DeclareMathOperator{\asech}{\sech^{-1}}
\DeclareMathOperator{\acsch}{\csch^{-1}}
\DeclareMathOperator{\acoth}{\coth^{-1}}
%    \end{macrocode}
% Next are some linear algebra keywords.
%    \begin{macrocode}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\realop}{Re}
\DeclareMathOperator{\imagop}{Im}
\newcommand{\real}[1]{\realop\{#1\}}
\newcommand{\imag}[1]{\imagop\{#1\}}
%    \end{macrocode}
% The sign and absolute value keywords:
%    \begin{macrocode}
\DeclareMathOperator{\sgn}{sgn}
\newcommand{\abs}[1]{\left\lvert#1\right\rvert}
%    \end{macrocode}
% Norm of a vector:
%    \begin{macrocode}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
%    \end{macrocode}
% Evaluation at endpoints uses |\left.| to get no visible mark on the left side.
%    \begin{macrocode}
\newcommand{\evalat}[3]{\left.#1\right|_{#2}^{#3}}
%    \end{macrocode}
% Poisson brackets are just braces
%    \begin{macrocode}
\newcommand{\pbrac}[2]{\left\{#1,#2\right\}}
\newcommand{\pbracvars}[4]{\left\{#1,#2\right\}_{#3,#4}}
%    \end{macrocode}
% This handles the redefinition of |\vec|. If the |boldvectors| option was passed,
% a vector is denoted by bolding the argument. If |arrowvectors| was passed, the
% vector is denoted by putting an arrow over the argument.
% Some people use an undertilde, which will probably be added in the future.
%    \begin{macrocode}
\ifthenelse{\boolean{pboldvectors}}%
 {\renewcommand{\vec}[1]{\mathbf{#1}}}%
 {\renewcommand{\vec}[1]{\accentset{\rightharpoonup}{#1}}}
%    \end{macrocode}
% |\vecvar| is just a synonym for |\vec|
%    \begin{macrocode}
\newcommand{\vecvar}[1]{\vec{#1}}
%    \end{macrocode}
% |\tnsvar| always uses bold. Some people use undertildes, which will be added.
%    \begin{macrocode}
\newcommand{\tnsvar}[1]{\mathbf{#1}}
%    \end{macrocode}
% |\matvar| always uses bold.
%    \begin{macrocode}
\newcommand{\matvar}[1]{\mathbf{#1}}
%    \end{macrocode}
% |\identitym| is a bold $1$
%    \begin{macrocode}
\newcommand{\identitym}{\mathbf{1}}
%    \end{macrocode}
% |\determinant| uses vertical bars.
%    \begin{macrocode}
\newcommand{\determinant}[1]{\left\lvert#1\right\rvert}
%    \end{macrocode}
% |\trace| uses capital Tr.
%    \begin{macrocode}
\DeclareMathOperator{\trace}{Tr}
%    \end{macrocode}
% Now we get to some unit vectors, all just the relevant letter with a hat.
%    \begin{macrocode}
\newcommand{\unitd}{\hat{d}}
\newcommand{\unite}{\hat{e}}
\newcommand{\uniti}{\hat{i}}
\newcommand{\unitj}{\hat{j}}
\newcommand{\unitk}{\hat{k}}
\newcommand{\unitl}{\hat{\ell}}
\newcommand{\unitn}{\hat{n}}
\newcommand{\unitp}{\hat{p}}
\newcommand{\unitq}{\hat{q}}
\newcommand{\unitr}{\hat{r}}
\newcommand{\units}{\hat{s}}
\newcommand{\unitt}{\hat{t}}
\newcommand{\unitu}{\hat{u}}
\newcommand{\unitv}{\hat{v}}
\newcommand{\unitw}{\hat{w}}
\newcommand{\unitx}{\hat{x}}
\newcommand{\unity}{\hat{y}}
\newcommand{\unitz}{\hat{z}}
\newcommand{\unitphi}{\hat{\phi}}
\newcommand{\unitrho}{\hat{\rho}}
\newcommand{\unittheta}{\hat{\theta}}
\newcommand{\unitomega}{\hat{\omega}}
%    \end{macrocode}
% This turns any letter into a unit vector.
%    \begin{macrocode}
\newcommand{\unitvec}[1]{\hat{#1}}
%    \end{macrocode}
% |\udc| is just an upright (roman) d, and similarly for higher-order differentials.
%    \begin{macrocode}
\newcommand{\udc}{\mathrm{d}}
\newcommand{\uddc}{\mathrm{d}^2}
\newcommand{\udddc}{\mathrm{d}^3}
%    \end{macrocode}
% |\pdc| is just |\partial|, defined for similarity with |\udc|.
%    \begin{macrocode}
\newcommand{\pdc}{\partial}
\newcommand{\pddc}{\partial^2}
\newcommand{\pdddc}{\partial^3}
%    \end{macrocode}
% |\uds| is just like |\udc| but it includes a small space in front. If I can figure
% out how to do it I'll make the command autodetect the preceding character(s) and
% figure out whether to add the space or not.
%    \begin{macrocode}
\newcommand{\uds}{\,\mathrm{d}}
\newcommand{\udds}{\,\mathrm{d}^2}
\newcommand{\uddds}{\,\mathrm{d}^3}
%    \end{macrocode}
% |\pds| is also defined for similarity as just |\partial| with a space in front,
% although I'm not sure this one is really useful.
%    \begin{macrocode}
\newcommand{\pds}{\,\partial}
\newcommand{\pdds}{\,\partial^2}
\newcommand{\pddds}{\,\partial^3}
%    \end{macrocode}
% |\ud| typesets a derivative using |\udc|. Similarly for second and third derivatives.
%    \begin{macrocode}
\newcommand{\ud}[2]{\frac{\mathrm{d}#1}{\mathrm{d}#2}}
\newcommand{\udd}[2]{\frac{\mathrm{d}^2#1}{\mathrm{d} #2^2}}
\newcommand{\uddd}[2]{\frac{\mathrm{d}^3#1}{\mathrm{d} #2^3}}
%    \end{macrocode}
% |\pd| does the same for partial derivatives with |\pdc|.
%    \begin{macrocode}
\newcommand{\pd}[2]{\frac{\partial #1}{\partial #2}}
\newcommand{\pdd}[2]{\frac{\partial^2#1}{\partial #2^2}}
\newcommand{\pddd}[2]{\frac{\partial^3#1}{\partial #2^3}}
%    \end{macrocode}
% |\grad| typesets the gradient symbol, a nabla with an arrow over it (actually a harpoon).
% This is done the same way regardless of the |arrowvectors| or |boldvectors| setting.
%    \begin{macrocode}
\newcommand{\grad}{\accentset{\rightharpoonup}{\nabla}}
%    \end{macrocode}
% |\div| is the divergence, defined using |\grad|. Ordinarily |\div| stands for the
% division symbol but nobody really uses that, so I figured it's worth replacing.
%    \begin{macrocode}
\renewcommand{\div}{\grad\cdot}
%    \end{macrocode}
% |\curl| is done in the obvious way using |\grad|
%    \begin{macrocode}
\newcommand{\curl}{\grad\times}
%    \end{macrocode}
% |\lapl| is written without a harpoon since it's a scalar operator
%    \begin{macrocode}
\newcommand{\lapl}{\nabla^2}
%    \end{macrocode}
% |\conj| just puts a superscript star
%    \begin{macrocode}
\newcommand{\conj}[1]{{#1 ^{*}}}
%    \end{macrocode}
% |\herm| is the same thing but for operators or matrices, so with a dagger
%    \begin{macrocode}
\newcommand{\herm}[1]{{#1 ^{\dagger}}}
%    \end{macrocode}
% |\transpose| does the same with a $T$
%    \begin{macrocode}
\newcommand{\transpose}[1]{{#1 ^{T}}}
%    \end{macrocode}
% These set notations are mostly done with |\mathbb|
%    \begin{macrocode}
\newcommand{\natset}{\mathbb{N}}
\newcommand{\intset}{\mathbb{Z}}
\newcommand{\cpxset}{\mathbb{C}}
\newcommand{\whlset}{\mathbb{Q}}
\newcommand{\realset}{\mathbb{R}}
\newcommand{\imagset}{\mathbb{I}}
%    \end{macrocode}
% Now Dirac notation, implemented using vertical bars and angle brackets in various combinations
%    \begin{macrocode}
\newcommand{\bra}[1]{\left\langle #1 \right\rvert}
\newcommand{\ket}[1]{\left\lvert #1 \right\rangle}
\newcommand{\braket}[2]{\langle #1 \vert #2 \rangle}
\newcommand{\melement}[3]{\langle #1 \vert #2 \vert #3 \rangle}
\newcommand{\projop}[2]{\vert #1 \rangle #2 \langle #1 \vert}
\newcommand{\expect}[1]{\left\langle #1 \right\rangle}
%    \end{macrocode}
% Commutators and anticommutators are done in the obvious way
%    \begin{macrocode}
\newcommand{\commut}[2]{\left[ #1, #2 \right]}
\newcommand{\acommut}[2]{\left\{ #1, #2 \right\}}
%    \end{macrocode}
% The |\round| operator just typesets the word ``round''
%    \begin{macrocode}
\DeclareMathOperator{\round}{round}
%    \end{macrocode}
% The exterior derivative is typeset in bold, in contrast to the differential $\udc$ which
% is just a plain roman font
%    \begin{macrocode}
\DeclareMathOperator{\exd}{\mathbf{d}}
%    \end{macrocode}
% The Hodge dual uses a star, but not superscript like |\conj|.
%    \begin{macrocode}
\newcommand{\hodge}{\star}
%    \end{macrocode}
% These are short macros to typeset the symbols for the elementary (and common non-elementary)
% particles. Each one is set in math roman font, as opposed to text roman font if it makes
% a difference. They're followed by an empty token |{}| for reasons which I forget.
%
% Theoretically these should only be loaded if the |particle| option was passed but I'll get
% to that later; in the meantime they're unlikely to conflict with anything important.
%    \begin{macrocode}
\newcommand{\upq}{\ensuremath{\mathrm{u}}{}}
\newcommand{\dnq}{\ensuremath{\mathrm{d}}{}}
\newcommand{\srq}{\ensuremath{\mathrm{s}}{}}
\newcommand{\chq}{\ensuremath{\mathrm{c}}{}}
\newcommand{\btq}{\ensuremath{\mathrm{b}}{}}
\newcommand{\tpq}{\ensuremath{\mathrm{t}}{}}
\newcommand{\upaq}{\ensuremath{\bar{\mathrm{u}}}{}}
\newcommand{\dnaq}{\ensuremath{\bar{\mathrm{d}}}{}}
\newcommand{\sraq}{\ensuremath{\bar{\mathrm{s}}}{}}
\newcommand{\chaq}{\ensuremath{\bar{\mathrm{c}}}{}}
\newcommand{\btaq}{\ensuremath{\bar{\mathrm{b}}}{}}
\newcommand{\tpaq}{\ensuremath{\bar{\mathrm{t}}}{}}
\newcommand{\elp}{\ensuremath{\mathrm{e}^-}{}}
\newcommand{\enu}{\ensuremath{\nu_\mathrm{e}}{}}
\newcommand{\ulp}{\ensuremath{\mu^-}{}}
\newcommand{\unu}{\ensuremath{\nu_{\mu}}{}}
\newcommand{\tlp}{\ensuremath{\tau^-}{}}
\newcommand{\tnu}{\ensuremath{\nu_{\tau}}{}}
\newcommand{\ealp}{\ensuremath{\mathrm{e}^+}{}}
\newcommand{\eanu}{\ensuremath{\bar{\nu}_\mathrm{e}}{}}
\newcommand{\ualp}{\ensuremath{\mu^+}{}}
\newcommand{\uanu}{\ensuremath{\bar{\nu}_{\mu}}{}}
\newcommand{\talp}{\ensuremath{\tau^+}{}}
\newcommand{\tanu}{\ensuremath{\bar{\nu}_{\tau}}{}}
\newcommand{\prbr}{\ensuremath{\mathrm{p}^+}{}}
\newcommand{\nebr}{\ensuremath{\mathrm{n}^0}{}}
\newcommand{\lmzbr}{\ensuremath{\Lambda^0}{}}
\newcommand{\sgpbr}{\ensuremath{\Sigma^+}{}}
\newcommand{\sgzbr}{\ensuremath{\Sigma^0}{}}
\newcommand{\sgmbr}{\ensuremath{\Sigma^-}{}}
\newcommand{\dlppbr}{\ensuremath{\Delta^{++}}{}}
\newcommand{\dlpbr}{\ensuremath{\Delta^+}{}}
\newcommand{\dlzbr}{\ensuremath{\Delta^0}{}}
\newcommand{\dlmbr}{\ensuremath{\Delta^-}{}}
\newcommand{\xizbr}{\ensuremath{\Xi^0}{}}
\newcommand{\ximbr}{\ensuremath{\Xi^-}{}}
\newcommand{\ommbr}{\ensuremath{\Omega^-}{}}
\newcommand{\sgspbr}{\ensuremath{\Sigma^{*+}}{}}
\newcommand{\sgszbr}{\ensuremath{\Sigma^{*0}}{}}
\newcommand{\sgsmbr}{\ensuremath{\Sigma^{*-}}{}}
\newcommand{\xiszbr}{\ensuremath{\Xi^{*0}}{}}
\newcommand{\xismbr}{\ensuremath{\Xi^{*-}}{}}
\newcommand{\prabr}{\ensuremath{\mathrm{p}^-}{}}
\newcommand{\neabr}{\ensuremath{\bar{\mathrm{n}}^0}{}}
\newcommand{\dlpabr}{\ensuremath{\bar{\Delta}^{+}}{}}
\newcommand{\dlzabr}{\ensuremath{\bar{\Delta}^{0}}{}}
\newcommand{\dlmabr}{\ensuremath{\bar{\Delta}^{-}}{}}
\newcommand{\dlmmabr}{\ensuremath{\bar{\Delta}^{--}}{}}
\newcommand{\pipm}{\ensuremath{\pi^+}{}}
\newcommand{\pizm}{\ensuremath{\pi^0}{}}
\newcommand{\pimm}{\ensuremath{\pi^-}{}}
\newcommand{\kapm}{\ensuremath{K^+}{}}
\newcommand{\kazm}{\ensuremath{K^0}{}}
\newcommand{\kazam}{\ensuremath{\bar{K}^0}{}}
\newcommand{\kamm}{\ensuremath{K^-}{}}
\newcommand{\ropm}{\ensuremath{\rho^+}{}}
\newcommand{\rozm}{\ensuremath{\rho^0}{}}
\newcommand{\romm}{\ensuremath{\rho^-}{}}
\newcommand{\etam}{\ensuremath{\eta}{}}
\newcommand{\etapm}{\ensuremath{\eta'}{}}
\newcommand{\kaspm}{\ensuremath{\mathrm{K}^{*+}}{}}
\newcommand{\kaszm}{\ensuremath{\mathrm{K}^{*0}}{}}
\newcommand{\kaszam}{\ensuremath{\bar{\mathrm{K}}^{*0}}{}}
\newcommand{\kasmm}{\ensuremath{\mathrm{K}^{*-}}{}}
\newcommand{\omm}{\ensuremath{\omega}{}}
\newcommand{\phim}{\ensuremath{\phi}{}}
\newcommand{\phbsn}{\ensuremath{\gamma}{}}
\newcommand{\Wbsn}{\ensuremath{\mathrm{W}}{}}
\newcommand{\Wpbsn}{\ensuremath{\mathrm{W}^{+}}{}}
\newcommand{\Wmbsn}{\ensuremath{\mathrm{W}^{-}}{}}
\newcommand{\Zzbsn}{\ensuremath{\mathrm{Z}^{0}}{}}
\newcommand{\hbsn}{\ensuremath{\mathrm{h}}{}}
\newcommand{\photon}{\phbsn}
%    \end{macrocode}
% The |feynman| option is implemented by just loading the package |feynmp|.
%    \begin{macrocode}
\ifthenelse{\boolean{pfeynman}}%
 {\RequirePackage{feynmp}}%
 {}
%    \end{macrocode}
%
% \pagebreak[2]
% \Finale