Geometric Representation of the generator of duality in massless and massive $p-$form field theories

TL;DR

This paper explores the geometric structure of duality symmetries in massless and massive p-form field theories, deriving Noether generators and extending the Loop Representation to provide a geometric interpretation.

Contribution

It introduces generalized geometric representations for duality generators in p-form theories, broadening the understanding of their symmetry structures.

Findings

Derived explicit form of duality generators

Extended Loop Representation to p-form fields

Provided geometric interpretation of duality transformations

Abstract

We study the invariance under duality transformations in massless and massive $p-$form field theories and obtain the Noether generators of the infinitesimal transformations that correspond to this symmetry. These generators are realized in geometrical representations that generalize the Loop Representation of the Maxwell field, allowing for a geometrical interpretation which is studied.