(1/2,1/2) Representation space: An ab initio construct

TL;DR

This paper provides an ab initio analysis of the (1/2,1/2) Lorentz representation space, revealing it as a spin-parity multiplet that naturally bifurcates into triplet and singlet states, challenging traditional spin interpretations.

Contribution

It introduces a new wave equation for the (1/2,1/2) multiplet and shows particles in this space do not have definite spin but definite relative intrinsic parity.

Findings

The (1/2,1/2) space is a spin-parity multiplet with bifurcation into triplet and singlet.

The textbook spin separation occurs only in limited kinematic conditions.

Scalar particles like the Higgs naturally inhabit this representation space.

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 text-book separation into spin one and spin zero 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 one and spin zero 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.