Lagrange Brackets and U(1) fields

TL;DR

This paper extends the concept of Lagrange Brackets to include U(1) gauge fields in p-brane theories, highlighting reparametrisation invariance and covariance under field redefinitions.

Contribution

It introduces a new formulation of brane Lagrangians incorporating U(1) fields using Lagrange and Poisson brackets, enhancing symmetry properties.

Findings

Lagrangians constructed with F_{ij} using Lagrange Brackets

Reparametrisation invariance explicitly manifest

Covariance under field redefinition achieved

Abstract

The idea of a companion Lagrangian associated with $p$-Branes is extended to include the presence of U(1) fields. The Brane Lagrangians are constructed with $F_{ij}$ represented in terms of Lagrange Brackets, which make manifest the reparametrisation invariance of the theory; these are replaced by Poisson Brackets in the companion Lagrangian, which is now covariant under field redefinition. The ensuing Lagrangians possess a similar formal structure to those in the absence of an anti-symmetric field tensor.