The Gauss Law Operator Algebra and Double Commutators in Chiral Gauge Theories

TL;DR

This paper uses an algebraic BJL method to compute anomalous Schwinger terms in fermionic current algebra within chiral gauge theories, resolving Jacobi identity violations and linking non-iterative terms to gauge group representations.

Contribution

It introduces a refined algebraic approach that accounts for equal-time subtleties, ensuring consistent current algebra in chiral gauge theories.

Findings

Resolved Jacobi identity violations in current algebra

Linked double commutator terms to gauge group projective representations

Provided a consistent algebraic framework for chiral gauge theories

Abstract

We calculate within an algebraic Bjorken-Johnson-Low (BJL) method anomalous Schwinger terms of fermionic currents and the Gauss law operator in chiral gauge theories. The current algebra is known to violate the Jacobi identity in an iterative computation. Our method takes the subtleties of the equal-time limit into account and leads to an algebra that fulfills the Jacobi identity. The non-iterative terms appearing in the double commutators can be traced back directly to the projective representation of the gauge group.