Simplifying Algebra in Feynman Graphs, Part III: Massive Vectors

TL;DR

This paper introduces a simplified, chirally minimized Feynman rule formalism for massive vector fields, enabling more efficient calculations in spontaneously broken gauge theories and related models.

Contribution

It develops a T-dualized, selfdual inspired formulation with a double line approach for massive vectors, reducing complexity in perturbative calculations.

Findings

Derived new Feynman rules with minimized spin indices

Formulated cross-sections using the new approach

Produced a dualized electroweak model

Abstract

A T-dualized selfdual inspired formulation of massive vector fields coupled to arbitrary matter is generated; subsequently its perturbative series modeling a spontaneously broken gauge theory is analyzed. The new Feynman rules and external line factors are chirally minimized in the sense that only one type of spin index occurs in the rules. Several processes are examined in detail and the cross-sections formulated in this approach. A double line formulation of the Lorentz algebra for Feynman diagrams is produced in this formalism, similar to color ordering, which follows from a spin ordering of the Feynman rules. The new double line formalism leads to further minimization of gauge invariant scattering in perturbation theory. The dualized electroweak model is also generated.