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.

应用 Duffin-Kemmer-Petiau (DKP) 代数的 Clifford 代数公式将 De Donder-Weyl Hamiltonian (DWH) 理论重铸为独立于 DKP 代数的矩阵表示的代数描述。我们证明了反对称场的 DWH 方程是由 DKP 代数对 Clifford 代数的某些不变子空间的作用产生的，这些不变子空间带有场的表示。还导出了与 DWH 方程的 DKP 形式相关的括号的无矩阵表示公式。该括号满足泊松括号的标准属性的一般化。