All Questions
Tagged with quantum-anomalies mathematical-physics
15 questions
1
vote
0
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40
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Axial anomaly for odd dimension
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space)...
- 91
1
vote
1
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235
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Is Weyl transformation part of diffeomorphism? Does a gravitational anomaly capture also the anomaly due to Weyl transformation? [duplicate]
Weyl transformation is a local rescaling of the metric tensor
$$
g_{ab}\rightarrow e^{-2\omega(x)}g_{ab}
$$
Diffeomorphism maps to a theory under arbitrary differentiable coordinate transformations
(...
- 4,376
4
votes
1
answer
225
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A critical step in Fujikawa's proof of the Atiyah Singer index theorem
If the Riemannian curvature is zero and $\mathrm{dim}(M)=n=2k$, the Atiyah-Singer index theorem for the twisted Dirac operator reduces to the following equation:
\begin{equation}\tag{1}
\mathrm{ind}(...
- 1,911
6
votes
1
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213
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Can a QFT be anomaly-free on spacetimes that are boundaries but still have an anomaly on other spacetimes?
If $D$ is the Dirac operator for some dynamic spinor fields in background gauge and gravitational fields, then the partition function is supposed to be $\mathrm{det}(D)$. For this to make sense, we ...
- 55k
3
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0
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92
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The sign of axion $F$ $F$ dual term in Weinberg
Related to the earlier question $\gamma^5$ rotation of chiral fermion in (1) Peskin&Schroeder, (2) Weinberg, or (3) Srednicki.
The sign of axion $F$ $F$ dual term in Weinberg (23.6.16) appears to ...
- 4,376
2
votes
0
answers
166
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Exotic perturbative anomaly captured only by higher-loop Feynman graphs, but not by any 1-loop Feynman graph?
My question: Are there any perturbative anomaly captured by higher-loop but not by captured at the 1-loop Feynman graph (say, not enough)?
We are familiar with the text book example of a ...
- 4,376
8
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2
answers
3k
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Weyl anomaly in 2d CFT (string theory lectures by D.Tong)
In his lectures on String Theory (http://www.damtp.cam.ac.uk/user/tong/string.html), Tong gives a proof of the Weyl anomaly, using equation $(4.37)$. It seems wrong to me.
Here he uses the OPE between ...
- 116
2
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1
answer
277
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axial anomaly for adjoint fermion v.s. fundamental fermion
It is known that the axial anomaly (chiral anomaly, the left L- right R) shows that $U(1)_A$-axial symmetry is not a global symmetry at quantum level.
In particular, one can consider the (1) ...
- 4,376
9
votes
1
answer
271
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How do anomalies work in the causal formulation of QFT?
In the Epstein-Glaser formulation of a QFT, the would-be divergences are taken care of by meticulously splitting the distributions that appear in the construction of the $S$-matrix (or correlation ...
3
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177
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't Hooft twisted torus construction and its relation to characteristic (e.g. Stiefel-Whitney) class [closed]
It is known that the $PSU(2) = SO(3)$ and there is an associated global anomaly labeled by the second Stiefel-Whitney class $w_2$.
This second Stiefel-Whitney class $w_2$ can detect the 1+1 ...
- 7,928
2
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1
answer
394
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Anomaly in quantum mechanics in path-integral formulation
If $A$ is a classical symmetry, it is possible that after quantization $A$ is no longer a symmetry. One of the ways to see this in the operator formulation of quantum mechanics is the following.
Let ...
- 231
4
votes
1
answer
277
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Anomalies and determinant bundle curvature
I heard that anomalies and curvature of determinant bundle are related. Namely, curvature of determinant bundle is related to Chern-Simons form (which are involved in description of gauge anomalies).
...
- 546
12
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1
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2k
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The index of a Dirac operator and its physical meaning
I recently read Witten's paper from the 1980s and he often uses the notion of the index of a Dirac operator in K-theory.
What is the meaning of the index of a Dirac operator?
What exactly is the ...
- 3,662
18
votes
3
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2k
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Homotopy $\pi_4(SU(2))=\mathbb{Z}_2$
Recently I read a paper using $$\pi_4(SU(2))=\mathbb{Z}_2.$$ Do you have any visualization or explanation of this result?
More generally, how do physicists understand or calculate high dimension ...
- 1,012
25
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4
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8k
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Where is the Atiyah-Singer index theorem used in physics?
I'm trying to get motivated in learning the Atiyah-Singer index theorem. In most places I read about it, e.g. wikipedia, it is mentioned that the theorem is important in theoretical physics. So my ...
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