Clifford Algebraic approach to the De Donder-Weyl Hamiltonian theory

TL;DR

This paper introduces a Clifford algebraic formulation of the De Donder-Weyl Hamiltonian theory, providing an algebraic, matrix-independent approach that generalizes the Poisson bracket for antisymmetric fields.

Contribution

It develops a matrix representation-free Clifford algebraic framework for the DWH theory, extending the DKP algebra application to field equations.

Findings

Derived a matrix-free formula for the DKP bracket.

Showed DWH equations emerge from DKP algebra acting on invariant subspaces.

Generalized the Poisson bracket properties within this algebraic context.

Abstract

The Clifford algebraic formulation of the Duffin-Kemmer-Petiau (DKP) algebras is applied to recast the De Donder-Weyl Hamiltonian (DWH) theory as an algebraic description independent of the matrix representation of the DKP algebra. We show that the DWH equations for antisymmetric fields arise out of the action of the DKP algebra on certain invariant subspaces of the Clifford algebra which carry the representations of the fields. The matrix representation-free formula for the bracket associated with the DKP form of the DWH equations is also derived. This bracket satisfies a generalization of the standard properties of the Poisson bracket