Inhomogeneous transformations in a gauged twistor formulation of a massive particle

TL;DR

This paper demonstrates that extending the local U(2) symmetry to IU(2) in a gauged twistor formulation automatically incorporates all mass-shell constraints into the action for a massive particle.

Contribution

It introduces an inhomogeneous extension of the local U(2) symmetry, IU(2), to automatically include mass-shell constraints in the twistor formulation.

Findings

Mass-shell constraints are incorporated via IU(2) symmetry.

Extension to IU(2) simplifies the formulation.

All necessary constraints are embedded in the action.

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.