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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 of the generalized phase space proposed by
Bohm and Hiley. Our development is based on the algebraic calculus introduced by Schönberg
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.