(1/2, 1/2) representation space - An ab initio construct
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abstract
A careful ab initio construction of the finite-mass (1/2, 1/2) representation space of the Lorentz group reveals it to be a spin-parity multiplet. In general, it does not lend itself to a single-spin interpretation. We find that the (1/2, 1/2) representation space for massive particles naturally bifurcates into a triplet and a singlet of opposite relative intrinsic parties. The textbook separation into spin-1 and spin-0 states occurs only for certain limited kinematical settings. We construct a wave equation for the (1/2, 1/2) multiplet, and show that the particles and antiparticles in this representation space do not carry a definite spin but only a definite relative intrinsic parity. In general, both spin-1 and spin-0 are covariantly inseparable inhabitants of massive vector fields. This last observation suggests that scalar particles, such as the Higgs, are natural inhabitants of massive (1/2, 1/2) representation space.
