Canonical Reduction of Symplectic Structures for the Maxwell and Yang-Mills Equations. Part 1

TL;DR

This paper applies a canonical reduction algorithm to Maxwell and Yang-Mills equations viewed as Hamiltonian systems, revealing geometric origins of the minimum interaction principle within the reduction process.

Contribution

It introduces a geometric reduction method for analyzing Maxwell and Yang-Mills equations as Hamiltonian systems, highlighting the geometric basis of the minimum interaction principle.

Findings

Reduction algorithm applied to gauge field equations

Revealed geometric origin of the minimum interaction principle

Established a framework for symplectic and connection structures in gauge theories

Abstract

The canonical reduction algorithm is applied to Maxwell and Yang-Mills equations considered as Hamiltonian systems on some fiber bundles with symplectic and connection structures. The minimum interaction principle proved to have geometric origin within the reduction method devised.