Inhomogeneous transformations in a gauged twistor formulation of a massive particle

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.