Clifford Algebraic approach to the De Donder-Weyl Hamiltonian theory

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