Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics

TL;DR

This paper develops a specialized Riemann-Hamilton geometric framework for polymomentum Hamiltonian systems in multi-time electrodynamics, incorporating d-connection, d-torsion, and d-curvature concepts.

Contribution

It introduces a distinguished Riemann-Hamilton geometry tailored for polymomentum Hamiltonians in multi-time electrodynamics, including Maxwell-like and Einstein-like equations.

Findings

Formulation of d-Riemannian geometry for polymomentum Hamiltonian

Derivation of geometrical Maxwell-like equations

Derivation of Einstein-like equations in this framework

Abstract

In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.