Galilean Duffin–Kemmer–Petiau algebra and symplectic structure

Abstract

We develop the Duffin–Kemmer–Petiau (DKP) approach in the phase-space picture of quantum mechanics by considering DKP algebras in a Galilean covariant context. Specifically, we develop an algebraic calculus based on a tensor algebra defined on a five-dimensional space which plays the role of spacetime background of the non-relativistic DKP equation. The Liouville operator is determined and the Liouville–von Neumann equation is written in two situations: the free particle and a particle in an external electromagnetic field. A comparison between the non-relativistic and the relativistic cases is commented.