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Spin degrees of freedom incorporated in conformal group: Introduction of an intrinsic momentum operator

Seiichi Kuwata

SciPost Phys. Proc. 14, 034 (2023) · published 24 November 2023

Proceedings event

34th International Colloquium on Group Theoretical Methods in Physics


Considering spin degrees of freedom incorporated in the conformal generators, we introduce an intrinsic momentum operator $\pi_\mu$, which is feasible for the Bhabha wave equation. If a physical state $\psi_{ph}$ for spin s is annihilated by the $\pi_\mu$, the degree of $\psi_{ph}$, deg $\psi_{ph}$, should equal twice the spin degrees of freedom, $2 ( 2 s + 1)$ for a massive particle, where the multiplicity $2$ indicates the chirality. The relation deg $\psi_{ph}$ = 2(2s+1) holds in the representation $R_5$ (s,s), irreducible representation of the Lorentz group in five dimensions.

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