dorsal/arxiv
View SchemaSpin and Statistics in Classical Mechanics
| Authors | J. A. Morgan |
|---|---|
| Categories | |
| ArXiv ID | physics/0401070 |
| URL | https://arxiv.org/abs/physics/0401070 |
| DOI | 10.1119/1.1778392 |
| Journal | Am.J.Phys.72:1408,2004 |
Abstract
The spin-statistics conection 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. Classical realizations of Lie groups can be constructed in a canonical formalism generalized to include Grassmann variables. The theory of irreducible canonical realizations of the Poincare group is developed in this framework, with particular emphasis on the rotation subgroup. The behavior of irreducible realizations under time inversion and charge conjugation is obtained. The requirement that the Lagrangian retain its form under the cominbed operation CT leads directly to the spin-statistics connection, by an adaptation of Schwinger's 1951 proof to irreducible canonical realizations of the Poincare group of spin j: Generalized spin coordinates and momenta satisfy fundamental Poisson bracket relations for 2j=even, and fundamental Poisson antibracket relations for 2j=odd.
{
"annotation_id": "deafb5cf-2a38-4100-8c4d-ff3ff72ad065",
"date_created": "2026-03-02T18:00:49.118000Z",
"date_modified": "2026-03-02T18:00:49.118000Z",
"file_hash": "2ecd8ea9a174165c66bf2748c6c58db2a0b3622c35181ddb0ac0f31cfd5eb4e4",
"private": false,
"record": {
"abstract": "The spin-statistics conection is obtained for classical point particles. The\nconnection holds within pseudomechanics, a theory of particle motion that\nextends classical physics to include anticommuting Grassmann variables, and\nwhich exhibits classical analogs of both spin and statistics. Classical\nrealizations of Lie groups can be constructed in a canonical formalism\ngeneralized to include Grassmann variables. The theory of irreducible canonical\nrealizations of the Poincare group is developed in this framework, with\nparticular emphasis on the rotation subgroup. The behavior of irreducible\nrealizations under time inversion and charge conjugation is obtained. The\nrequirement that the Lagrangian retain its form under the cominbed operation CT\nleads directly to the spin-statistics connection, by an adaptation of\nSchwinger\u0027s 1951 proof to irreducible canonical realizations of the Poincare\ngroup of spin j: Generalized spin coordinates and momenta satisfy fundamental\nPoisson bracket relations for 2j=even, and fundamental Poisson antibracket\nrelations for 2j=odd.",
"arxiv_id": "physics/0401070",
"authors": [
"J. A. Morgan"
],
"categories": [
"physics.class-ph",
"physics.gen-ph"
],
"doi": "10.1119/1.1778392",
"journal_ref": "Am.J.Phys.72:1408,2004",
"title": "Spin and Statistics in Classical Mechanics",
"url": "https://arxiv.org/abs/physics/0401070"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e041c74e-97f5-44fc-b943-68869070952a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}