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 had ronic quantum theory, we present a derivation of the DKP equation on the ge neralized phase space proposed by Bohm and Hiley. Our development is based on the algebraic calculus introduced by Schonberg and uses the idea of alge braic spinors due to Riesz and Cartan. The free DKP particle and the more g eneral case of the DKP particle in a prescribed external electromagnetic fi eld are considered, and we obtain the DKP Liouville type equations for thes e cases.