All Questions
11
questions
3
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0
answers
77
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Application of Callias operator in physics
In his article "Axial Anomalies and Index Theorems on Open Spaces" C.Callias shows how the index of the Callias-type operator on $R^{n}$ can be used to study properties of fermions in the ...
- 31
1
vote
0
answers
40
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Regarding vanishing of a triangle diagram
Furry's theorem ($C$ symmetry) is very important in calculations in QCD, Electroweak theory. Primarily it says everything about QED (three photon triangle diagram), but can be extended to QCD, and ($Z$...
- 534
2
votes
1
answer
121
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Why does fermion have the expansion with Grassmann-numbers?
I learn the chiral anomaly by Fujikawa method. The text book "Path Integrals and Quantum Anomalies, Kazuo Fujikawa", in the page 151, says that
…one can define a complete orthonormal set $\{...
- 129
0
votes
1
answer
365
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Chiral symmetry of the Euclidean action for fermions
In the literature, such as QFT Volume-II by Weinberg, p.368, the chiral anomaly is derived using Euclidean path integral. To formulate the question, let's start with the Minkowski space with signature ...
2
votes
1
answer
347
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Chiral anomaly: UV or IR effect
In TASI 2003 Lectures on Anomalies (section 1.6) Jeffrey A. Harvey present arguments, why chiral anomaly is IR effect (in contrast to calculation, where UV regulator was used):
Only massless ...
- 5,707
7
votes
2
answers
2k
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Anomaly inflow mechanism
I know very simple example of anomaly inflow. See section 4.4 in David Tong: Lectures on Gauge Theory. As I read, such mechanism have some applications in condensed matter and in quantum field theory, ...
- 5,707
0
votes
0
answers
226
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Peskin equation on the treatment of chiral anomaly
In page 666 (it couldn't be other way - bad joke), chapter 19, the Eq. (19.73) claims (see properties of the $\phi_n(x)$ functions in this post: Change of variables in path integral measure):
$$
\...
- 1,597
8
votes
1
answer
529
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Does the massless fermion in $2+1$ dimensions suffer from gauge anomaly?
In Fermion Path Integrals And Topological Phases Witten showed that for a massless Dirac fermion in $2+1$ dimensions
$$S[\bar{\psi},\psi]=\int d^{3}x\bar{\psi}iD\!\!\!\!/_{A}\psi,$$
where $A$ is a $...
- 2,923
11
votes
2
answers
1k
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Parity Anomaly and Gauge Invariance
In Fermionic Path Integral and Topological Phases, Witten shows that in $2+1$ dimensions, the free massless Dirac fermion suffers from parity anomaly. To be specific, he shows that it is impossible to ...
- 2,923
5
votes
1
answer
711
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Anomaly cancellation and fermion number violation
In the standard model, an axial $SU(3)$ currents has anomaly which after quantization leads to the fermion number violation. However, taking all the fermions into account we note that the anomalies ...
- 104
13
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2
answers
1k
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On the Axial Anomaly
I know that if we start with a massive theory, the chiral states $L$ and $R$ remain coupled to each other in the massless limit. Because a charged Dirac particle of a given helicity can make a ...
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