Classical Isometrodynamics

TL;DR

This paper develops a new gauge theory called Isometrodynamics by extending non-Abelian gauge theories to volume-preserving diffeomorphisms of a D-dimensional space, deriving its Lagrangian, dynamics, and Hamiltonian.

Contribution

It introduces a novel gauge theory based on non-compact volume-preserving diffeomorphisms, expanding the framework of gauge theories beyond Lie groups.

Findings

Derived the invariant gauge field Lagrangian.

Established classical dynamics and conservation laws.

Formulated the Hamiltonian in axial gauge.

Abstract

A generalization of non-Abelian gauge theories of compact Lie groups is developed by gauging the non-compact group of volume-preserving diffeomorphisms of a $D$-dimensional space R^D. This group is represented on the space of fields defined on M^4 x R^D. As usual the gauging requires the introduction of a covariant derivative, a gauge field and a field strength operator. An invariant and minimal gauge field Lagrangian is derived. The classical field dynamics and the conservation laws of the new gauge theory are developed. Finally, the theory's Hamiltonian in the axial gauge and its Hamiltonian field dynamics are derived.