Consistent and Covariant Commutator Anomalies in the Chiral Schwinger Model

✍ Scribed by Christoph Adam

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 284 KB
• Volume: 265
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1997.5769

✦ Synopsis

We derive all covariant and consistent divergence and commutator anomalies of chiral QED 2 within the framework of canonical quantization of the fermions. Further, we compute the time evolution of all occurring operators and find that all commutators evolve canonically. We comment on the relation of our results to the finding of a nontrivial U(1)-curvature in gauge-field space.

1998 Academic Press

1. Introduction

Chiral gauge theories are anomalous when the fermions are quantized. These anomalies have several, well-known consequences. The divergence of the gauge current deviates from its canonical value by a certain polynomial in the gauge field (anomaly'') [1 4]. Further, the commutators of charge densities [5] and of the generators of time-independent gauge transformations (the Gauss law operators'') [6 8] acquire anomalous contributions, also. While there is some arbitrariness in the choice of regularization for the currents, leading to different forms of the anomalies and anomalous commutators, we shall study two well-known versions: the consistent ones (obeying a consistency condition) [9] and the covariant ones (resulting from a covariant regularization) [10]. All these anomalies are determined by geometrical or cohomological considerations [6, 7, 11 13].

However, whereas the complete Gauss law commutator is fixed in this way, the situation is less clear for the individual components of the Gauss law operator G (we use the notation (x 0 , x 1 )#({, _) and, frequently, (A 0 , A 1