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

Abstract

FSU TPI 11/99 hep-th/9911175We 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 matrices β µ (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 as the covariant Poisson brackets given by β-matrices and the corresponding Poisson bracket formulation of DW Hamiltonian field equations.In the end of the thirties is was observed [1] (see [2] for historical details) that the first order form of the Klein-Gordon and the Proca field equations can be represented in the Dirac-like matrix formwhere β-matrices fulfill the relationwhich defines the so-called Duffin-Kemmer-Petiau (DKP) algebra (for a textbook introduction see, e.g., [3,4]). Later on similar considerations have been extended to higher-spin theories [5][6][7], gauge fields [9,8], curved space-time [10], and even to the Einstein gravity [9,11] and arbitrary non-linear equations (see [4,9,11] and the references therein). From a more mathematical point of view DKP algebras have been considered, e.g., in [7,[12][13][14]. *

A Teoria de Duffin-Kemmer-Petiau

“…Na física nuclear, a teoria ainda têm se mostrado profícua no que concerneà fenomenologia, uma vez que a vasta gama de interações presentes na teoria de DKP são impossíveis de serem expressas pelas teorias de Klein-Gordon-Fock ou Proca [29]. A teoria de DKP também experimentou novo fôlego no contexto de aplicações em cromodinâmica quântica em curtas e longas distâncias por Gribov [30], no espalhamento de núcleos K + [31], dinâmica hamiltoniana covariante [32], espaço-tempo curvo [33], invariância de Galileu em cinco dimensões [34], no contexto da invariância de gauge clássica [35], no método causal de Epstein-Glaser [36] e, sistematicamente, no estudo de espalhamento e confinamento de partículas [37].…”

Cartan gravity, matter fields, and the gauge principle

“…An approach sharing features of the approach chosen in this paper and in [6] is the Duffin-KemmerPetiau (DKP) formulation of Klein-Gordon and vector field equations [31,32,33,34,35]. As is the case for field equations recovered from polynomially simple actions, the DKP field equations are first order in spacetime derivatives.…”

Duffin-Kemmer-Petiau equation in Robertson-Walker space-time

“…Recently, there has been an increasing interest in DKP theory in curved space-time [29][30][31][32][33]. To our knowledge, there are only a few available exact solutions and less discussions in the context of DKP gravitational with mass.…”