Pseudoclassical model of a particle with arbitrary spin

“…An earlier paper 1 presented a classical analog of the spin-statistics connection for pseudomechanics, a version of analytical dynamics containing even and odd Grassmann variables. 2,3,4,5,6,7 The method of proof relies on the canonical formalism for fields, suitably extended to include odd Grassmann variables. Classical field theory is readily cast in terms of the canonical formalism, 8,9,10 most familiarly as part of many an introductory account of quantum field theory.…”

Section: Introductionmentioning

confidence: 99%

The spin-statistics connection in classical field theory

Morgan¹

2006

J. Phys. A: Math. Gen.

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The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group corresponding to general causal fields is reviewed. The connection is obtained by imposing local commutativity on the fields and exploiting the parity operation to exchange spatial coordinates in the scalar product of classical field evaluated at one spatial location with the same field evaluated at a distinct location. The spin-statistics connection for irreducible canonical realizations of the Poincaré group of spin j is obtained in the form: Classical fields and their conjugate momenta satisfy fundamental field-theoretic Poisson bracket relations for 2j even, and fundamental Poisson antibracket relations for 2j odd.

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“…Due to the reparametrizations in all the cases Hamiltonian equal zero on the constraint surface. In the papers [10][11][12], devoted to the quantization of these models, they tried to avoid these difficulties, using the so called Dirac method of quantization of theories with first-class constraints [13], in which one considers the first-class constraints in the sense of restrictions on the state vectors. Unfortunately, in general case, this scheme of quantization creates many questions, e.g.…”

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confidence: 99%

Quantization of a Pseudoclassical Model of the Spin 1 Relativistic Particle

Гитман

Gonçalves

Tyutin

1995

Int. J. Mod. Phys. A

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A consistent procedure of canonical quantization of pseudoclassical model for spin one relativistic particle is considered. Two approaches to treat the quantization for the massless case are discussed, the limit of the massive case and independent quantization of a modified action. Quantum mechanics constructed for the massive case proves to be equivalent to the Proca theory and for massless case to the Maxwell theory. Results obtained are compared with ones for the case of spinning (spin one half) particle.

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Pseudoclassical model of a particle with arbitrary spin

Cited by 7 publications

References 14 publications

Spin and statistics in classical mechanics

Spin and statistics in classical mechanics

The spin-statistics connection in classical field theory

Quantization of a Pseudoclassical Model of the Spin 1 Relativistic Particle

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