Duffin--Kemmer--Petiau subalgebras: representations and applications

A reduction of the Duffin-Kemmer-Petiau algebra to a direct sum of irreducible subalgebras for spin-0 and spin-1 bosons is presented. The subalgebras are defined by multiplication rules for the linearly independent basis elements. In the representations discussed the spin projection operators are independent basis elements of the subalgebras. The formal utility of these representations is demonstrated by obtaining the reduction of arbitrary operator products and trace theorems. The practical utility is demonstrated by application to the analysis of free and interacting boson field currents. Most importantly, one can understand the differences between DKP nonconserved currents and those obtained from second-order wave equations.