Consistent and Covariant Commutator Anomalies in the Chiral Schwinger Model

Abstract

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

Electrodynamics in a Background Chiral Field

“…The two dimensional limit of massive electrodynamics has been considered in refs. [22,23]. If there is an axial coupling between the spinor and an external axial field, this leads to the one-loop effective action…”

Covariant Stora–Zumino chain terms

“…as may be checked easily (see also [17], journal version). Here the exponential is defined as its power series, and the derivative is understood in an algebraic sense, e.g., v(δ/δA)P (A) = P (A + v)| v 1 (i.e., the component of P (A + v) linear in v).…”

“…There are several methods for the computation of anomalies, anomalous commutators (Schwinger terms) and higher terms of the Stora-Zumino chain, both for the consistent and covariant case. Among these are perturbative, functional and algebraic methods [1]- [17] (see [18] for a review).…”

Exploring anomalies by many-body correlations

“…The anomalies lead to anomalous Ward identities 28,29 and destroy the gauge invariance 6,30 seen also in trace anomalies 31 . One can either formulate the theory consistent or covariant [32][33][34][35][36] dependent whether one accepts alternatively violation of gauge invariance or violation of conservation laws. Furthermore the acceptance of anomalies does not guarantee renormalizability of the theory 37,38 .…”