Fields on Paracompact Manifold and Anomalies

TL;DR

This paper discusses the mathematical treatment of scalar and Dirac fields on paracompact manifolds within continuum light cone quantization, providing a gauge-invariant method to compute triangle anomalies.

Contribution

It extends the operator distribution approach to QED Dirac fields on paracompact manifolds, simplifying anomaly calculations.

Findings

Test functions as decomposition of unity facilitate anomaly calculations

Gauge-invariant treatment of Dirac fields in QED

Simplified computation of triangle anomalies

Abstract

In Continuum Light Cone Quantization (CLCQ) the treatment of scalar fields as operator valued distributions and properties of the accompanying test functions are recalled. Due to the paracompactness property of the Euclidean manifold these test functions appear as decomposition of unity. The approach is extended to QED Dirac fields in a gauge invariant way. With such test functions the usual triangle anomalies are calculated in a simple and transparent way.