Relativistic wave equations: proper Lorentz invariance and invariance under discrete transformations

Abstract

Considering the standard form i∂ψ/∂t = Hψ [with ψ transforming according to D(0,s)⊕D(s,0)] of wave equations for free particles of arbitrary spin, we determined in a recent paper the admissible forms of H consistent with invariance of the equation under the Poincarè group and under T, C, and P. Here we show that even if T and C invariance is not imposed, the admissible Hamiltonians are the same (apart from one extra possibility H = E). Expressed differently, except for the trivial case H = E, invariance of free-particle equations under the connected Poincarè group and P implies T and C also.