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 is there no anomaly when particle mechanics is quantized?
We know that if one or more symmetries of the action of a classical field theory is violated in its quantized version the corresponding quantum theory is said to have anomaly.
Is this a sole feature ...
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Anomalies and Modification of symmetry algebra
This question is motivated by 2-dimensional CFTs where the Classical conformal group (defined by the Witt algebra) is modified to the Virasoro algebra in the quantum theory. In this question, it was ...
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Why are topological properties described by surface terms?
An example are the anomalies in abelian and non-abelian gauge quantum field theories.
For example, the abelian anomaly is $\tilde {F}_{\mu\nu}F^{\mu\nu}$ and the integral over this quantity is a ...
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Point splitting technique in Peskin and Schroeder
One of the cornerstones of point splitting technique of calculating chiral anomaly (Peskin and Schroeder 19.1, p.655) is a symmetric limit $\epsilon \rightarrow 0$. And this is the point that I don't ...
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Why do we solve the Wess-Zumino consistency condition using the method of descent?
Consider a quantum field theory in $d$ dimensions with a symmetry $G$. For the purpose of this discussion let's say that $d$ is even and $G$ is a compact, connected Lie group. We say that the symmetry ...
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For the $U(1)$ problem, is the Kugo and Ojima Goldstone quartet wrong?
On page 96 in "Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem", Prog. Theor. Phys. Suppl. 66 (1979) 1, KO state the following:
Finally we should ...
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Identically vanishing trace of $T^{\mu\nu}$ and trace anomaly
Let us consider a theory defined by an action on a flat space $S[\phi]$ where $\phi$ denotes collectively the fields of the theory. We will study the theory on a general background $g_{\mu\nu}$ and ...
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What exactly is a gauge anomaly?
In lots of papers I read about gauge anomalies. For example, avoiding gauge anomalies in the MSSM is the reason for introducing an extra Higgs doublet. Gauge anomalies in the Standard Model are ...
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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 ...
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Simple explanation of chiral anomaly?
Can somebody provide a fairly brief explanation of what the chiral anomaly is? I have been unable to find a concise reference for this. I know QFT at the P&S level so don't be afraid to use math.
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When is an anomaly one-loop exact?
There are many examples of quantum anomalies that are one-loop exact, and many examples of anomalies that have contributions to all orders in perturbation theory. I haven't been able to identify a ...
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Why is the chiral symmetry $SU(2)_A$ not anomalous?
Using Fujikawa's path integral treatment of the triangle diagram, one can show that
$$\mathrm{Tr} \gamma^5 = \int d^4 x\ \partial_{\mu}j^{\mu} $$
Where $j^{\mu}$ is the Noether current of $U(1)_A$. ...
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What really enforces technical naturalness of electron mass?
Technical or 't Hooft naturalness A parameter $\theta$ in the Lagrangian of a field theory is said to be natural, if in the limit of vanishing $\theta$, the theory has some enhanced symmetry. If this ...
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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 ...
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Mathematically rather than physically speaking, is there something "special" about 10 (or 11) dimensions?
As I understand it, string theory (incorporating bosons and fermions) "works" in $9+1=10$ spacetime dimensions. In the context of dual resonance theory, I've read descriptions of why that is "...
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