summaryrefslogtreecommitdiff
path: root/support/hypertex/tanmoy/examples/Anomalkap.aux
blob: 98d88ee63f76a525d165d0c0663a3f6c3aa90adc (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
\relax 
\citation{KP}
\citation{Jan}
\citation{CS}
\citation{KP}
\citation{FS}
\citation{Neu}
\citation{Neu2}
\citation{AK}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {i}}{\hbox {\hskip 1pt\relax \uppercase {i}}}\hskip -1pt\relax }Introduction}{3}}
\newlabel{sec:int}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {i}}{\uppercase {i}}}{3}}
\citation{KP}
\citation{Alt}
\citation{Dis}
\citation{CS}
\citation{Neu}
\citation{Neu}
\citation{Sham}
\citation{chiral}
\citation{Neu}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {ii}}{\hbox {\hskip 1pt\relax \uppercase {ii}}}\hskip -1pt\relax }Action, Fermion Propagator and Chiral Zero Modes}{5}}
\newlabel{sec:model}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {ii}}{\uppercase {ii}}}{5}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{A}{\hbox {\hskip 1pt\relax A}}\hskip -1pt\relax }Lattice Action}{5}}
\citation{Neu}
\citation{KP}
\citation{Neu}
\citation{Dis}
\citation{Neu}
\citation{Neu}
\citation{Alt}
\newlabel{actionf}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{3}{3}}{6}}
\citation{Neu}
\citation{CS}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{B}{\hbox {\hskip 1pt\relax B}}\hskip -1pt\relax }Chiral Zero Modes}{7}}
\citation{Neu}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{C}{\hbox {\hskip 1pt\relax C}}\hskip -1pt\relax }Fermion Propagator and Zero Modes}{8}}
\newlabel{fprop}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{11}{11}}{8}}
\newlabel{gl}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{13}{13}}{8}}
\citation{Neu}
\citation{Neu}
\citation{CS}
\newlabel{gr}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{14}{14}}{9}}
\citation{Sham}
\citation{Sham}
\citation{Dis}
\newlabel{wil}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{17}{17}}{10}}
\newlabel{shl}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{18}{18}}{10}}
\newlabel{shr}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{19}{19}}{10}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{D}{\hbox {\hskip 1pt\relax D}}\hskip -1pt\relax }Fermion Feynman Rules }{10}}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {iii}}{\hbox {\hskip 1pt\relax \uppercase {iii}}}\hskip -1pt\relax }Perturbative Calculations for the Chiral Schwinger Model}{11}}
\newlabel{sec:2dim}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {iii}}{\uppercase {iii}}}{11}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{A@}{\hbox {\hskip 1pt\relax A}}\hskip -1pt\relax }Effective Action at Fermion One-Loop}{12}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{B@}{\hbox {\hskip 1pt\relax B}}\hskip -1pt\relax }Evaluation of Zero Mode Contributions}{12}}
\citation{Dis}
\newlabel{sumf}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{37}{37}}{14}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{C@}{\hbox {\hskip 1pt\relax C}}\hskip -1pt\relax }Evaluation of Remaining Contributions}{14}}
\newlabel{gcs}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{39}{39}}{14}}
\citation{CS}
\citation{CS}
\newlabel{sum}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{41}{41}}{15}}
\newlabel{cst}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{42}{42}}{15}}
\citation{FS}
\citation{Neu,AK}
\citation{chiral}
\citation{Dis}
\citation{chiral}
\newlabel{sumk}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{44}{44}}{16}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{D@}{\hbox {\hskip 1pt\relax D}}\hskip -1pt\relax }Total Contributions}{16}}
\newlabel{eff}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{45}{45}}{16}}
\citation{Neu}
\citation{Neu2}
\citation{JR}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {iv}}{\hbox {\hskip 1pt\relax \uppercase {iv}}}\hskip -1pt\relax }Anomalies in the Chiral Schwinger Model}{17}}
\newlabel{sec:anomaly}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {iv}}{\uppercase {iv}}}{17}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{A@@}{\hbox {\hskip 1pt\relax A}}\hskip -1pt\relax }Currents and their Divergence}{17}}
\newlabel{current}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{49}{49}}{18}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{B@@}{\hbox {\hskip 1pt\relax B}}\hskip -1pt\relax }Gauge invariance}{18}}
\newlabel{sum0a}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{52}{52}}{18}}
\citation{Jan}
\newlabel{sum0b}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{equation}{53}{53}}{19}}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{C@@}{\hbox {\hskip 1pt\relax C}}\hskip -1pt\relax }Gauge Anomalies}{19}}
\citation{KP,CS}
\citation{CS}
\citation{CS}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{D@@}{\hbox {\hskip 1pt\relax D}}\hskip -1pt\relax }Chern-Simons Current}{20}}
\citation{CS}
\citation{Dis}
\citation{KP,Jan,Dis}
\citation{Dis}
\@writefile{toc}{\string\contentsline\space {subsection}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{subsection}{E}{\hbox {\hskip 1pt\relax E}}\hskip -1pt\relax }Pythagorean Chiral Schwinger Model and Anomaly in Fermion Number Current}{21}}
\citation{Dis}
\citation{Neu}
\citation{AK}
\citation{Dis}
\citation{chiral}
\@writefile{toc}{\string\contentsline\space {section}{\string\numberline\space {\relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {v}}{\hbox {\hskip 1pt\relax \uppercase {v}}}\hskip -1pt\relax }conclusions}{23}}
\newlabel{sec:concl}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{section}{\uppercase {v}}{\uppercase {v}}}{23}}
\citation{Neu}
\citation{Neu3}
\citation{Neu2}
\bibcite{KP}{1}
\bibcite{Jan}{2}
\bibcite{CS}{3}
\bibcite{FS}{4}
\bibcite{Neu}{5}
\bibcite{Neu2}{6}
\bibcite{AK}{7}
\bibcite{Alt}{8}
\bibcite{Dis}{9}
\bibcite{Sham}{10}
\bibcite{chiral}{11}
\bibcite{JR}{12}
\bibcite{Neu3}{13}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {1}{\ignorespaces  Two zero modes $u_L$ and $u_R$ as a function of $s$ at $m_0=0.1$ and 0.5 for $p_1=p_2=0$. We take $L=100$.}}{26}}
\newlabel{zero}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{figure}{1}{1}}{26}}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {2}{\ignorespaces  The coefficient of the anomaly $C(s)$ for the Kaplan's method as a function of $s$ at $m_0=0.1$ and 0.5 for $L=100$.}}{26}}
\newlabel{anomalyK}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{figure}{2}{2}}{26}}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {3}{\ignorespaces  The coefficient of the anomaly $C(s)$ for the Shamir's method as a function of $s$ at $m_0=0.1$ and 0.5 for $L=100$.}}{26}}
\newlabel{anomalyS}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{figure}{3}{3}}{26}}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {4}{\ignorespaces The coefficient of the Chern-Simons current $I(s)$ for the Kaplan's method as a function of $s$ at $m_0=0.1$ and 0.5 for $L=100$.}}{26}}
\newlabel{CSK}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{figure}{4}{4}}{26}}
\@writefile{lof}{\string\contentsline\space {figure}{\string\numberline\space {5}{\ignorespaces  The coefficient of the Chern-Simons current $I(s)$ for the Shamir's method as a function of $s$ at $m_0=0.1$ and 0.5 for $L=100$.}}{26}}
\newlabel{CSS}{{\relax \let \hyper@@@ \relax \let \hyper@@@ \relax \let \hyper@@@ \hyper@ \hyperpr@ref {}{figure}{5}{5}}{26}}