On the Duffin-Kemmer Algebra

Hitherto unnoticed algebraical features of the Duffin-Kemmer algebra, the so-called meson algebra, have been exhaustively brought to light in the general case of n dimensions. Stress is laid on treating it quite generally as an abstract algebra rather than as a matric algebra, so that no reference is made to explicit representations. The main point consists in explicit construction of the 2n+1Cn linearly independent bases of the algebra each transforming as an antisymmetric tensor for all orthogonal transformations of the n-dimensional β-space. From the physical point of view this tensor character is of paramount importance, for it enables one to get an adequate apparatus for extracting any component from the wave function and accordingly to manifest the direct correspondence between the two alternative modes of formulation of meson theory, the particle formulation and the more usual wave formulation. Recently A. Klein has proposed an interesting procedure to extract a specific component from the meson wave function, which is now shown to be derivable from the present standpoint and at the same time a considerable amount of information is newly obtained in the Dirac algebra.