On the Duffin-Kemmer-Petiau algebra and the generalized phase space

The Duffin-Kemmer-Petiau (DKP) relativistic equation has been recently uded to study the interactions of spinless mesons with nuclei. In view of this interest and also the interest to determine the phase space picture for hadronic quantum theory, we present a derivation of the DKP equation on the generalized phase space proposed by Bohm and Hiley. Our development is based on the algebraic calculus introduced by Schonberg and uses the idea of algebraic spinors due to Riesz and Cartan. The free DKP particle and the more general case of the DKP particle in a prescribed external electromagnetic field are considered, and we obtain the DKP Liouville type equations for these cases.