Anomalies in gauge theories

Research output: Contribution to journalReview articlepeer-review

94 Scopus citations

Abstract

We discuss the scale and chiral anomalies in quantum chromodynamics and their implications for the theory of hadrons. In the first part the physical meaning of the anomaly is demonstrated. To this end the simplest gauge model is considered - the two-dimensional Schwinger model. In this model it is extremely easy to explain which properties of the theory are responsible for the quantum anomaly, and the physical nature of the phenomenon is elucidated. The second part is devoted to the derivation of the anomaly relations within QCD. The subtle question of the multiloop corrections is discussed. The third part presents applications. Starting from the chiral and scale anomalies we obtain low-energy theorems which lead, in turn, to predictions for observable processes. In particular, a proof based on first principles is given of the existence of massless pions, the amplitudes are calculated for the conversion of gluon operators into pions, which can be measured experimentally. Other practical problems are also considered, the solution of which turns out to be possible due to anomalies.

Original languageEnglish (US)
Pages (from-to)341-378
Number of pages38
JournalPhysics Reports
Volume209
Issue number6
DOIs
StatePublished - Dec 1991

Bibliographical note

Funding Information:
** Work supported in part by Schweizenscher Nationalfonds. Permanent address.

Fingerprint Dive into the research topics of 'Anomalies in gauge theories'. Together they form a unique fingerprint.

Cite this