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

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.

6 pages, LaTeX2e

References in corpus (6)

• Canonical Structure of Classical Field Theory in the Polymomentum Phase Space
• On Field Theoretic Generalizations of a Poisson Algebra
• DeDonder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory
• Generally relativistical Daffin-Kemmer formalis and behaviour of quantm-mechanical particle of spin 1 in the Abelian monopole field
• Duffin-Kemmer-Petiau equation in Riemannian space-times
• On the bracket problem in covariant Hamiltonian field theory

Cited by in corpus (24)

• On the nonminimal vector coupling in the Duffin-Kemmer-Petiau theory and the confinement of massive bosons by a linear potential
• The DKP oscillator with a linear interaction in the cosmic string space-time
• Interacting spin 0 fields with torsion via Duffin-Kemmer-Petiau theory
• Bose-Einstein Condensation and Free DKP field
• Spin 1 fields in Riemann-Cartan space-times "via" Duffin-Kemmer-Petiau theory
• Precanonical Quantum Gravity: quantization without the space-time decomposition
• Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field
• Cartan gravity, matter fields, and the gauge principle
• Exact Solution of Photon Equation in Stationary Gödel-type and Gödel Space-Times
• De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity
• Spin-zero system of DKP equation in the background of a flat class of Gödel-type space-time
• Lorentz-violating extension of the spin-one Duffin-Kemmer-Petiau equation
• Schrödinger wave functional in quantum Yang-Mills theory from precanonical quantization
• A discrete model of the Dirac-Kähler equation
• Aharonov-Bohm effect on the generalized Duffin-Kemmer-Petiau oscillator in the Som-Raychaudhuri space-time
• On the Equivalence of the Massless DKP equation and the Maxwell Equations in the Shuwer
• The spin-one DKP Equation with a nonminimal vector interaction in the presence of minimal uncertainty in momentum
• Exact Solutions of the Photon Equation in Anisotropic Spacetimes
• Three dimensional DKP oscillator in a curved Snyder space
• Scalar Quantum Electrodynamics via Duffin-Kemmer-Petiau Gauge Theory in the Heisenberg Picture:Vacuum Polarization
• Schrödinger Functional of a Quantum Scalar Field in Static Space-Times from Precanonical Quantization
• Clifford Algebraic approach to the De Donder-Weyl Hamiltonian theory
• Precanonical structure of the Schrödinger wave functional in curved space-time
• Exact Solutions of the DKP Oscillator in 3D Spaces with Extended Uncertainty Principle