A New Approach to Axial Vector Model Calculations II

TL;DR

This paper advances a novel method for calculating heat kernels in fermionic theories with vector and axial vector fields, deriving a master formula for one-loop amplitudes and extending the approach to various field theory contexts.

Contribution

It develops a new approach to heat kernel calculations, deriving a master formula for one-loop amplitudes with vector and axial vector fields in any even dimension.

Findings

Derived a Bern-Kosower type master formula for one-loop amplitudes.

Extended the method to massless and off-diagonal heat kernels in four dimensions.

Applied techniques to include external fermions and isospin in the formalism.

Abstract

We further develop the new approach, proposed in part I (hep-th/9807072), to computing the heat kernel associated with a Fermion coupled to vector and axial vector fields. We first use the path integral representation obtained for the heat kernel trace in a vector-axialvector background to derive a Bern-Kosower type master formula for the one-loop amplitude with $M$ vectors and $N$ axialvectors, valid in any even spacetime dimension. For the massless case we then generalize this approach to the full off-diagonal heat kernel. In the D=4 case the SO(4) structure of the theory can be broken down to $SU(2) \times SU(2)$ by use of the 't Hooft symbols. Various techniques for explicitly evaluating the spin part of the path integral are developed and compared. We also extend the method to external fermions, and to the inclusion of isospin. On the field theory side, we obtain an extension of the second order formalism for fermion QED to an abelian vector-axialvector theory.