Galilean covariance and non-relativistic Bhabha equations

We apply a five-dimensional formulation of Galilean covariance to construct non-relativistic Bhabha first-order wave equations which, depending on the representation, correspond either to the well known Dirac equation (for pa rticles with spin 1/2) or the Duffin-Kemmer-Petiau equation (for spinless a nd spin 1 particles). Here the irreducible representations belong to the Li e algebra of the 'de Sitter group' in 4 + 1 dimensions, SO (5, 1). Using th is approach, the nonrelativistic limits of the corresponding equations are obtained directly, without taking any low-velocity approximation. As a simp le illustration, we discuss the harmonic oscillator.