Canonical formalism and quantization of a massless spinning bosonic particle in four dimensions

Deguchi, Shinichi; Negishi, Shouma; Okano, Satoshi; Suzuki, Takafumi

doi:10.1142/s0217751x14500444

Cited by 6 publications

(15 citation statements)

References 39 publications

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“…This action describes a free massless spinning particle of helicity s [22][23][24] and is equivalent to the action for a massless particle with rigidity at least at the classical mechanical level [25]. 5 From the actionSmg, the Pauli-Lubanski spin vector W αα is found to be…”

Section: Construction Of the Ggs Actionmentioning

confidence: 99%

“…In this paper, we consider an alternative generalization of the Shirafuji action to define a new twistor model of a free massive spinning particle in four dimensions by using two twistors. Our formulation is precisely a non-Abelian extension of the gauged twistor formulation of a free massless spinning particle in four dimensions [22][23][24]. In the gauged twistor formulation, the Shirafuji action is modified in accordance with the gauge principle so that it can become invariant under the local U (1) (phase) transformation of twistor variables.…”

Section: Introductionmentioning

confidence: 99%

“…From the point of view of twistor theory, it is desirable that the modified action remains invariant under the combination of the local U (1) and local scale transformations, which is referred to in Refs. [23,24] as the complexified local scale transformation. In actuality, the gauge field for the local scale transformation can be gauged away by a scaling of the twistor variables.…”

Section: Introductionmentioning

confidence: 99%

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Gauged twistor formulation of a massive spinning particle in four dimensions

Deguchi

Okano

2016

Phys. Rev. D

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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.

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Section: Construction Of the Ggs Actionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gauged twistor formulation of a massive spinning particle in four dimensions

Deguchi

Okano

2016

Phys. Rev. D

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“…Our description of spin on the base of vector variables gives one more example of physically interesting noncommutative relativistic particle, with the "parameter of noncommutativity" proportional to spin-tensor. There are other examples where the noncommutative geometry emerges from second-class constraints, see [35][36][37][38][39][40][41][42][43][44].…”

Section: Jhep03(2014)109mentioning

confidence: 99%

Frenkel electron and a spinning body in a curved background

Ramírez

Дериглазов

Pupasov-Maksimov

2014

J. High Energ. Phys.

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We develop a variational formulation of a particle with spin in a curved spacetime background. The model is based on a singular Lagrangian which provides equations of motion, a fixed value of spin and Frenkel condition on spin-tensor. Comparing our equations with those of Papapetrou we conclude that the Frenkel electron in a gravitational field has the same behavior as a rotating body in the pole-dipole and leading-spin approximation. Due to constraints presented in the formulation, position space is endowed with a noncommutative structure induced by the spin of the particle. Therefore, the model provides a physically interesting example of a noncommutative particle in a curved background.

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“…It was demonstrated in Ref. [18] that the action S with m = 0 is equivalent to the gauged Shirafuji action [19][20][21] (rather than the original Shirafuji action [22]) that governs a twistor model of a massless spinning particle of helicity k propagating in 4dimensional Minkowski space, M. The gauged Shirafuji action can thus be regarded as a twistor representation of the action for a massless particle with rigidity. Upon canonical quantization of the twistor model, the allowed values of k are restricted to either integer or half-integer values, which are in agreement with the allowed values obtained in Ref.…”

Section: Introductionmentioning

confidence: 99%

Twistor formulation of a massive particle with rigidity

Deguchi

Suzuki

2018

Nuclear Physics B

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A massive rigid particle model in (3 + 1) dimensions is reformulated in terms of twistors.Beginning with a first-order Lagrangian, we establish a twistor representation of the Lagrangian for a massive particle with rigidity. The twistorial Lagrangian derived in this way remains invariant under a local U (1) × U (1) transformation of the twistor and other relevant variables.Considering this fact, we carry out a partial gauge-fixing so as to make our analysis simple and clear. We develop the canonical Hamiltonian formalism based on the gauge-fixed Lagrangian and perform the canonical quantization procedure of the Hamiltonian system. Also, we obtain an arbitrary-rank massive spinor field in (3+1) dimensions via the Penrose transform of a twistor function defined in the quantization procedure. Then we prove, in a twistorial fashion, that the spin quantum number of a massive particle with rigidity can take only non-negative integer values, which result is in agreement with the one shown earlier by Plyushchay. Interestingly, the mass of the spinor field is determined depending on the spin quantum number.

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Canonical formalism and quantization of a massless spinning bosonic particle in four dimensions

Cited by 6 publications

References 39 publications

Gauged twistor formulation of a massive spinning particle in four dimensions

Gauged twistor formulation of a massive spinning particle in four dimensions

Frenkel electron and a spinning body in a curved background

Twistor formulation of a massive particle with rigidity

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