Generators of the Poincaré Group for arbitrary tensors and spinor-tensors

Abstract

In this work, we systematically derive explicit expressions for the Poincaré Group generators on arbitrary-rank tensors and spinor-tensors in D=3+1 and D=2+1 spacetimes, thus generalizing previous works in the literature for the groups ISO(3,1) and ISO(2,1). From the Casimir eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli constraints for massive particles for spins s=5/2, 3, and 4 in D=3+1 and helicities α=5/2, 3, and 4 in D=2+1 dimensions. We also comment on the demonstration of the Fierz-Pauli constraints for the general case of arbitrary spin (helicity).