On the Duffin-Kemmer-Petiau Formulation of the Covariant Hamiltonian Dynamics in Field Theory

TL;DR

This paper demonstrates that the De Donder-Weyl covariant Hamiltonian equations can be expressed in Duffin-Kemmer-Petiau matrix form, revealing universal significance of DKP matrices across various fields in covariant Hamiltonian field theory.

Contribution

It introduces a DKP matrix formulation for DW Hamiltonian equations, extending their applicability beyond scalar fields and establishing a link to symplectic structures in field theory.

Findings

DKP matrices can represent DW Hamiltonian equations for all fields.

DKP beta-matrices are universal and analogous to symplectic matrices.

Brief discussion on covariant Poisson brackets using beta-matrices.

Abstract

We show that the De Donder-Weyl (DW) covariant Hamiltonian field equations of any field can be written in Duffin-Kemmer-Petiau (DKP) matrix form. As a consequence, the (modified) DKP beta-matrices (5 X 5 in four space-time dimensions) are of universal significance for all fields admitting the DW Hamiltonian formulation, not only for a scalar field, and can be viewed as field theoretic analogues of the symplectic matrix, leading to the so-called ``k-symplectic'' (k=4) structure. We also briefly discuss what could be viewed as the covariant Poisson bracket given by beta-matrices and the corresponding Poisson bracket formulation of DW Hamiltonian field equations.