BRS Operators and Covariant Derivatives in Loop Space for P-Branes Coupled to Yang-Mills

TL;DR

This paper develops canonical forms for BRS operators and covariant derivatives in loop space for p-branes, extending the mathematical framework for analyzing their gauge symmetries and dynamics.

Contribution

It introduces a general method to construct canonical forms of BRS operators and covariant derivatives in loop space for all odd p-branes, enhancing the theoretical toolkit.

Findings

Canonical forms for BRS operators are provided for all odd p.

The covariant loop space derivative commutes with the BRS operator.

Methods for constructing these canonical forms are discussed.

Abstract

Canonical forms are given for the nilpotent BRS operator $\d$ and the covariant `loop space' derivative ${\cal D}_{\m}$ for the p-brane fields for all odd p. The defining characteristic of ${\cal D}_{\m}$ is that it is a functional derivative operator which generalizes the ordinary functional derivative and also commutes with $\d$. Methods of construction for the canonical forms are discussed.