Poincaré algebra massless representations

Abstract

The zero-mass, discrete-spin, representations of the Poincare algebra are found. They are not decomposable so their bases are connections, not tensors, giving gauge invariance (a partial statement of Poincare invariance) which occurs only for zero mass. Spin m and representation dimension 1 are related by m = ( 1 2 ) (1−1) ; the photon has three (not four) components. The potential (a connection not a tensor), being measurable and transforming under a Poincare algebra irreducible representation, both unlike the (auxillary, non-gauge invariant) electromagnetic field, is the fundamental object. A magnetic monopole would violate Poincare invariance--a good reason for its nonexistence.