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arXiv · 2606.02477

Parity Oddness of $\operatorname{Spin}(1,4)$ Dirac Mass Terms

Craig McRae
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Abstract

In the representation theory of Lorentzian orthogonal groups there are well known arguments as to why the parity operator $\mathcal{P}$ and the time reversal operator $\mathcal{T}$ should be realized as linear and anti-linear operators respectively (Wigner 1932). In this paper it is shown that the only operators satisfying the requisite properties for the spinor representation of the de Sitter group $\operatorname{SO}(1,4)$ lead to fermion self-couplings which are necessarily parity odd, ruling out standard Dirac mass terms for theories with fermions obeying $\operatorname{Spin}(1,4)$ symmetry.

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Craig McRae. 2026-06-01. Parity Oddness of $\operatorname{Spin}(1,4)$ Dirac Mass Terms. https://arxiv.org/abs/2606.02477

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