Spin and statistics in classical mechanics

Morgan, J. A.

doi:10.1119/1.1778392

Cited by 6 publications

(6 citation statements)

References 65 publications

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“…Actually, since 1965 more than a hundred publications appeared deriving the spin-statistics connection under different sets of conditions [6]. Reviews are contained in [7][8][9][10]. Many of these publications derive the connection in settings far removed from standard (local) relativistic quantum field theory; and they are also far from simple and easy.…”

Section: Introductionmentioning

confidence: 99%

Connecting Spin and Statistics in Quantum Mechanics

Jabs

2009

Found Phys

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Abstract. The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spinquantization axis, is exchanged along with the other parameters. The spin factor (−1) 2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required.

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Section: Introductionmentioning

confidence: 99%

Connecting Spin and Statistics in Quantum Mechanics

Jabs

2009

Found Phys

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“…1,23,24 The familiar c-number bosonic variables of traditional classical physics are even Grassmann variables. Odd classical Grass-mann variables anticommute in a form of the exclusion principle.…”

Section: Classical Grassmann Fieldsmentioning

confidence: 99%

“…The commutation properties of Grassmann variables permit the realization of ferminonic and bosonic exchange symmetry in a classical setting. 1,23,24 The familiar c-number bosonic variables of traditional classical physics are even Grassmann variables. Odd classical Grass-mann variables anticommute in a form of the exclusion principle.…”

Section: Classical Grassmann Fieldsmentioning

confidence: 99%

“…Fix a common origin for both r and r ′′ . The frame r ′′ is assumed to differ from r by a rotation defined by Euler angles α, β, γ. Denote the action of the rotation that carries r to r ′′ by the rotation operator D (1) (α β γ) and that which carries ξ to ξ ′′ by D (0) (α β γ):…”

Section: Classification Of Irreducible Realizations Of the Poincaré G...mentioning

confidence: 99%

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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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“…This view of spin is now known to be unacceptable because the speed of rotation required to produce the known electron magnetic moment is much greater than the speed of light [3]. However the spin operator does obey nonrelativistic angular momentum commutation relations which has led to a number of researchers putting forward models of spin based on the classical notion of rotation [4,5]. Spin does not arise naturally in nonrelativistic quantum mechanics; it was introduced phenomenologically by Pauli into nonrelativistic quantum theory.…”

Section: Introductionmentioning

confidence: 99%

Angular momentum of a relativistic wave packet

Strange

2017

Phys. Rev. A

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Strange, Paul (2017) Angular momentum of a relativistic wave packet. Physical Review A: Atomic, Molecular and Optical Physics, 96 (5 Quantum-mechanical spin is often thought of in terms of classical angular momentum. In fact spin is defined by its commutation relations and the spin and orbital angular momentum operators are very different. Here we solve the Dirac equation in a rotating frame of reference and create a localized wave packet from the resulting wave functions to examine the consequences of the rotational motion. We highlight some unexpected effects in the properties of the wave packet and show that the spin operator and orbital angular momentum operator describe different aspects of the rotational properties of the wave packet. It is also observed that neither quantum-mechanical spin nor orbital angular momentum can be fully understood within an inertial frame.

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Spin and statistics in classical mechanics

Abstract: The spin-statistics connection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which exhibits classical analogs of both spin and statistics.

Cited by 6 publications

References 65 publications

Connecting Spin and Statistics in Quantum Mechanics

Connecting Spin and Statistics in Quantum Mechanics

The spin-statistics connection in classical field theory

Angular momentum of a relativistic wave packet

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