- AMER PHYSICAL SOC
We present a gauged twistor model of a free massive spinning particle in four-dimensional Minkowski space. This model is governed by an action, referred to here as the gauged generalized Shirafuji (GGS) action, that consists of twistor variables, auxiliary variables, and U(1) and SU(2) gauge fields on the onedimensional parameter space of a particle's worldline. The GGS action remains invariant under reparametrization and the local U(1) and SU(2) transformations of the relevant variables, although the SU(2) symmetry is nonlinearly realized. We consider the canonical Hamiltonian formalism based on the GGS action in the unitary gauge by following Dirac's recipe for constrained Hamiltonian systems. It is shown that just sufficient constraints for the twistor variables are consistently derived by virtue of the gauge symmetries of the GGS action. In the subsequent quantization procedure, these constraints turn into simultaneous differential equations for a twistor function. We perform the Penrose transform of this twistor function to define a massive spinor field of arbitrary rank, demonstrating that the spinor field satisfies generalized Dirac-Fierz-Pauli equations with SU(2) indices. We also investigate the rank-one spinor fields in detail to clarify the physical meanings of the U(1) and SU(2) symmetries.
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- DOI : 10.1103/PhysRevD.93.045016
- ISSN : 2470-0010
- eISSN : 2470-0029
- Web of Science ID : WOS:000370028500005