On the Duffin-Kemmer-Petiau formulation of the covariant Hamiltonian dynamics in field theory

We show that the De Donder-Weyl (DW) covariant Hamiltonian field equations of any field can be written in universal Duffin-Kemmer-Petiau (DKP) matrix form. As a consequence, the (modified) DKP matrices βμ (5 × 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 “k-symplectic” (k=4) structure. We also briefly discuss what could be viewed to be the covariant Poisson bracket given by β-matrices and the corresponding Poisson bracket formulation of DW Hamiltonian field equations.