Sp(2) Covariant Quantisation of General Gauge Theories

TL;DR

This paper develops a covariant quantisation framework for gauge theories using Sp(2) symmetry, providing a geometric interpretation and applying it to complex theories like superparticles.

Contribution

It introduces a consistent Sp(2) covariant Lagrangian quantisation method for general gauge theories with a geometric perspective.

Findings

Formulated Sp(2) BRST invariant action for superparticle

Reviewed geometric interpretation of gauge theories

Established covariant quantisation for reducible gauge algebras

Abstract

This letter studies the Sp(2) covariant quantisation of gauge theories. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles $Q(M_S, G_S)$ is reviewed. It is then described the Sp(2) algebra of ordinary Yang-Mills theory. A consistent formulation of covariant lagrangian quantisation for general gauge theories based on Sp(2) BRST symmetry is established. The original N=1, ten dimensional superparticle is considered as an example of infinitely reducible gauge algebras, and given explicitly its Sp(2) BRST invariant action.