Gauge Theory by canonical Transformations

TL;DR

This paper presents a novel derivation of U(1)-gauge theory within a covariant Hamiltonian framework using canonical transformations, offering an alternative to traditional Lagrangian approaches.

Contribution

It introduces a formalism that derives gauge fields and their dynamics through canonical transformations, highlighting the gauge dependence of the gauge field Hamiltonian.

Findings

Derivation of U(1)-gauge theory using covariant Hamilton formalism

Canonical transformations formalize the gauging procedure

The form of the gauge field Hamiltonian depends on gauge dependence choice

Abstract

Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U(1)-gauge theory in a manifestly covariant Hamilton formalism. We make use of canonical transformations as our guiding tool to formalize the gauging procedure. The introduction of the gauge field, its transformation behaviour and a dynamical gauge field Lagrangian/Hamiltonian are unavoidable consequences of this formalism, whereas the form of the free gauge Lagrangian/Hamiltonian depends on the selection of the gauge dependence of the canonically conjugate gauge fields.