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 one-dimensional 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.

A twistor model of a free massless spinning particle in 4-dimensional Minkowski space is studied in terms of spacetime and spinor variables. This model is specified by a simple action, referred to here as the gauged Shirafuji action, that consists of twistor variables and gauge fields on the 1-dimensional parameter space. We consider the canonical formalism of the model by following the Dirac formulation for constrained Hamiltonian systems. In the subsequent quantization procedure, we obtain a planewave solution with momentum spinors. From this solution and coefficient functions, we construct positive-frequency and negative-frequency spinor wave functions defined on complexified Minkowski space. It is shown that the Fourier-Laplace transforms of the coefficient functions lead to the spinor wave functions expressed as the Penrose transforms of the corresponding holomorphic functions on twistor space. We also consider the exponential generating function for the spinor wave functions and derive a novel representation for each of the spinor wave functions. * )

It is proved that the n-twistor expression of a particle's four-momentum vector reduces, by a unitary transformation, to the two-twistor expression for a massive particle or the one-twistor expression for a massless particle. Therefore the genuine n-twistor description of a massive particle in four-dimensional Minkowski space fails for the case n ≥ 3.

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