Extension of the Shirafuji Model for Massive Particles With Spin

Abstract

We extend the Shirafuji model for massless particles with primary spacetime coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the spacetime four-vector, four scalars describing spin and charge degrees of freedom as well as a pair of Weyl spinors. The geometric description proposed in this paper provides an intermediate step between the free purely twistorial model in two-twistor space in which both spacetime and four-momenta vectors are composite, and the standard particle model, where both spacetime and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wavefunctions describing relativistic particles with mass, spin and electric charge. The spacetime coordinates in the model are not commutative; this leads to a wavefunction that depends only on one covariant projection of the spacetime fourvector (covariantized time coordinate) defining plane wave solutions.

A no-go theorem for the n-twistor description of a massive particle

“…In fact, Lagrangian mechanics of a massive spinning particle in M has been successfully formulated in Refs. [7][8][9][10][11][12][13][14][15][16][17] by using two twistors. In the respective formulations, the SU(2) symmetry in two-twistor system is maintained in the action of a massive spinning particle.…”

“…Long after Penrose, Perjés, and Hughston made their attempts, Lagrangian mechanics of a massive spinning particle in M has been formulated in terms of twistors, and it has been studied until quite recently [7][8][9][10][11][12][13][14][15][16][17]. In almost all these studies [7][8][9][10][11][12][13][14][15]17], only the two-twistor description of a massive particle is conventionally adopted without clarifying the reason why the n(≥ 3)-twistor description is not employed. Under such circumstances, Routh and Townsend showed that only the two-twistor formulation can successfully describe a massive particle in M [16].…”

Massive relativistic particle model with spin from free two-twistor dynamics and its quantization

“…[18]), as reflected by the non-vanishing of the PB among the spacetime coordinates of the particles with spin; this is also the case when spin is related to the pres-ence of the supersymmetry and the superspace extension of classical mechanics [19,20,21] . We see therefore two options for describing a two-twistor-inspired massive spinning particle dynamics: i) to use the standard Penrose approach with noncommutative Minkowski coordinates satisfying the PB (1.12) [21]. In such a case to complete the description of the quantized theory of particles with non-vanishing spin one is led to a field theoretic framework on noncommutative spacetime [37].…”

Model of massless relativistic particle with continuous spin and its twistorial description

“…In addition, the twistor approach is used not only for massless states of finite spin. For example, there are twistor formulations of massive particles with fixed spin (see, for example, [34,35,36,37] and references therein) as well as massive particles of higher spins [38].…”