Generalized U(N) gauge transformations in the realm of the extended covariant Hamilton formalism of field theory

TL;DR

This paper extends classical gauge theories by incorporating space-time curvature transformations within an extended Hamilton formalism, allowing gauge bosons to acquire mass without breaking gauge invariance.

Contribution

It introduces a generalized gauge transformation framework in the extended covariant Hamilton formalism, unifying gauge invariance with space-time curvature variations.

Findings

The Hamiltonian remains invariant under extended gauge transformations.

Massive gauge bosons can be consistent with gauge invariance.

The equations of motion align with Einstein and Proca equations for static fields.

Abstract

The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary particle interactions. In this paper, this principle is extended to require additionly the form-invariance of a classical field theory Hamiltonian under variations of the space-time curvature emerging from the gauge fields. This approach is devised on the basis of the extended canonical transformation formalism of classical field theory which allows for transformations of the space-time metric in addition to transformations of the fields. Working out the Hamiltonian that is form-invariant under extended local gauge transformations, we can dismiss the conventional requirement for gauge bosons to be massless in order for them to preserve the local gauge invariance.The emerging equation of motion for the curvature scalar turns out to be compatible with the Einstein equation in the case of a static gauge field. The emerging equation of motion for the curvature scalar R turns out to be compatible with that from a Proca system in the case of a static gauge field.