A New Approach to Axial Vector Model Calculations II

Details A New Approach to Axial Vector Model Calculations II A New Approach to Axial Vector Model Calculations II

1998-12-23

arxiv.org/abs/hep-th/9812213v2

JHEP 9903 (1999) 022

Physics

High Energy Physics

High Energy Physics - Theory

Sequel to hep-th/9807072, references added, some clarifications and corrections, 29 pages, RevTex, 8 diagrams using epsfig.sty

Scientific paper

10.1088/1126-6708/1999/03/022

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.

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