Physics Stack Exchange
Physics Stack Exchange

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.

This tag is for anomalies in a symmetry, either in classical or quantum theories.

DO NOT USE THIS TAG for anomalies in a measurement, e.g. the tag should not be used if the question deals with the Pioneer anomaly.

402 questions
103
votes
1 answer

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or points of view: Anomalies are due to the fact that quantum field theories (and maybe quantum mechanical theories…
Diego Mazón
  • 7,127
54
votes
2 answers

Symmetries of the Standard Model: exact, anomalous, spontaneously broken

There are a number of possible symmetries in fundamental physics, such as: Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and Lorentz invariance proper), conformal invariance (i.e.,…
Gro-Tsen
  • 850
38
votes
1 answer

Instantons, anomalies, and 1-loop effects

A symmetry is anomalous when the path-integral measure does not respect it. One way this manifests itself is in the inability to regularize certain diagrams containing fermion loops in a way compatible with the symmetry. Specifically, it seems…
user6013
  • 943
31
votes
1 answer

Why do we assume local conformal transformations are symmetries in 2D CFT?

The global conformal group in 2D is $SL(2,\mathbb{C})$. It consists of the fractional linear transforms that map the Riemann sphere into itself bijectively and is finite dimensional. However, when studying $CFT_2$ people always use the full…
Dan
  • 2,757
31
votes
2 answers

Central charge in a $d=2$ CFT

I've always been confused by this very VERY basic and important fact about two-dimensional CFTs. I hope I can get a satisfactory explanation here. In a classical CFT, the generators of the conformal transformation satisfy the Witt algebra $$[…
Prahar
  • 29,157
29
votes
1 answer

Can a theory gain symmetries through quantum corrections?

It is well known that not all symmetries are preserved when quantising a theory, as evinced by renormalising composite operators or by other means, which show that quantum corrections may alter a conservation law, such as with the chiral anomaly, or…
user2062542
  • 739
26
votes
4 answers

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 question is, what are some examples of these…
Eric
  • 1,804
23
votes
2 answers

Why do some anomalies (only) lead to inconsistent quantum field theories

In connection with Classical and quantum anomalies, I'd like to ask for a simple explanation why some anomalies lead to valid quantum field theories while some others (happily absent in the standard model) seem to make the corresponding quantum…
Arnold Neumaier
  • 46,304
21
votes
2 answers

The phrase "Trace Anomaly" seems to be used in two different ways. What's the relation between the two?

I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing. The first way I've seen it used is in the manner, for example, that is relevant for the a-theorem and…
user26866
  • 3,582
  • 26
  • 37
21
votes
1 answer

Quantum symmetries that are not classical symmetries

An anomaly is a symmetry of the classical action that fails to be a symmetry of the path integral, due to non-invariance of the path integral measure. Does it ever occur that the opposite thing happens, i.e. that the classical action does not…
asperanz
  • 4,538
20
votes
5 answers

Why does string theory require 9 dimensions of space and one dimension of time?

String theorists say that there are many more dimensions out there, but they are too small to be detected. However, I do not understand why there are ten dimensions and not just any other number? Also, if all the other dimensions are so coiled up…
James Kujareevanich
  • 877
19
votes
1 answer

What's the real resolution of the $U(1)_A$ problem?

To recap the problem, consider QCD with three massless quark flavors. There is a symmetry $$SU(3)_L \times SU(3)_R \times U(1)_L \times U(1)_R$$ corresponding to independent rotations of the left-chiral and right-chiral quark fields. Vector…
knzhou
  • 107,105
19
votes
2 answers

What is the difference between Chiral anomaly, ABJ anomaly, and Axial anomaly?

I get confuse with these three terms: Chiral anomaly, ABJ anomaly, and Axial anomaly. I can not find standard definition of these three. Is there anyone can describe precisely?
Eric
  • 199
18
votes
1 answer

't Hooft vs ABJ anomalies

At some point in our physics education, we begin to accumulate a bunch of slogans related to anomalies. At some (later, in my case) point, we learn that actually there were two different kinds of anomalies all along: 't Hooft and ABJ anomalies. We…
anon
18
votes
3 answers

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 homotopy group?
Yingfei Gu
  • 1,032
1
2 3
…
26 27