Inhomogeneous transformations in a gauged twistor formulation of a massive particle

TL;DR

This work shows that in a gauged twistor formulation for a massive spinning particle, promoting the internal symmetry from $U(2)$ to the inhomogeneous group $IU(2)$ automatically incorporates the mass-shell constraints into the action. By introducing an inhomogeneous transformation parameter $\Lambda(\tau)$ and adjusting the transformation rules for $h$, $\bar{h}$ and the phase $\varphi$, the authors construct an $IU(2)$-invariant action $S$ augmented by the mass-term combination $S_h$, such that all constraints arise from the symmetry principles rather than being imposed by hand. The key result is that mass-shell constraints become consequences of local $IU(2)$ invariance, providing a self-contained framework potentially simplifying the canonical quantization and gauge fixing of twistor-based descriptions of massive particles. The approach leverages a two-twistor system with a coset realization of $SU(2)/U(1)$, the introduction of one-dimensional gauge fields $a$, $b$, $h$, and $\bar{h}$, and a nonlinear realization of the internal symmetry, yielding a unified, symmetry-driven constraint structure with practical implications for quantization.

Abstract

In this paper, we show that the mass-shell constraints in the gauged twistor formulation of a massive particle given in [Deguchi and Okano, Phys. Rev. D 93, 045016 (2016) [Erratum 93, 089906(E) (2016)]] are incorporated in an action automatically by extending the local $U(2)$ transformation to its inhomogeneous extension denoted by $IU(2)$. Therefore, it turns out that all the necessary constraints are incorporated into an action by virtue of the local $IU(2)$ symmetry of the system.