Questions tagged [quantum-anomalies]
This tag is for anomalies in a symmetry, either in classical or quantum theories. DO NOT USE THIS TAG for anomalies in a measurement.
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Why are gauge anomalies characterised by the non-triviality of $\pi_5(\mathcal G)$?
The folklore in 4-dimensional gauge theories is that the existence of potential gauge anomalies from the triangle diagrams that need to be cancelled are characterised by the non-triviality of the ...
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Why are certain topological effects important in quantum theories but not in classical theories?
At the start of Tong's notes on gauge theory, he explains that in classical theory, electromagnetic potentials (or other gauge potentials) don't have any physical influence except through their field ...
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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 ...
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Why is it important that the vector current should be conserved in QED?
In Quantum Field Theory and the Standard Model by MD Schwartz in the chapter about the anomalies, he derives from the equation of motions and the Noether currents of a effective massless QED ...
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Anomalous Ward Identities and anomalous dimensions
Let us consider an action $S[\phi,\partial\phi]$ which is classically invariant under a transformation group $G$. The associated Noether current $\mathcal{J}^\mu$ is classically conserved, namely $\...
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Does the Coleman-Weinberg mechanism belong to the dynamical symmetry breaking or the anomaly?
We know that a massless $\phi^4$ theory
$$S=\int d^4x \left[\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{\lambda}{4!}\phi^4\right],$$
has conformal invariance at the classical level. But within ...
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How to calculate an axial anomaly in 1+1 dimensions?
As far as I understand, an axial $U(1)$ transformation transforms a two-component spinor like
$$ \psi \to \psi'=\text e^{\text i\epsilon \gamma^5 }\psi,\qquad \psi=\begin{pmatrix}\psi_1\\\psi_2\end{...
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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 ...
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Conformal theory with zero central charge
Suppose there is a conformal field theory which has the global conformal symmetry namely $SL(2,R).$ and after central extension it is enhanced to Virasoro algebra with central charge, $c=0$ (also ...
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Understanding typical non-perturbative calculations in QFT [closed]
Perturbative calculations in quantum field theory are based on S-matrix expansion and calculating the Feynman diagrams. These Feynman diagrams are related to the scattering cross-sections and decay ...
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How projective representations can lead to 't Hooft anomalies in quantum mechanics?
In Shao's talk https://youtu.be/2vTvHYYl1Qk?t=1554, he argues that in quantum mechanics "if a symmetry acts projectively on states, then we have a t' Hooft anomaly". But I'm having trouble ...
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Why is baryon or lepton violation in standard model is a non-perturbative effect?
The baryon number B or lepton number L violation in the standard model arise from triangle anomaly. Right? Triangle diagrams are perturbative diagrams. Then why the B or L violation in Standard model ...
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Zumino's consistent and covariant anomalies - applied to quantum hall?
What is the `physical' meaning of consistent anomalies and covariant anomalies?
Perhaps a good Reference is:
Consistent and covariant anomalies in gauge and gravitational theories -
William A. ...
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Why do we think that the $U(1)$ problem is solved by instantons?
It is usually thought that the $U(1)$ problem is solved when 't Hooft realized that instantons induce additional symmetry breaking of the $U(1)_A$ symmetry aside from the non-vanishing quark masses. ...
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Does Leptogenesis require lepton number violating vertices?
One of the Sakharov condition for Baryogenesis requires Baryon number violating interactions in the theory. However, it is also possible to generate a baryon asymmetry via a lepton asymmetry or ...
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