dorsal/arxiv
View SchemaThe spin-statistics connection in classical field theory
| Authors | J. A. Morgan |
|---|---|
| Categories | |
| ArXiv ID | physics/0601014 |
| URL | https://arxiv.org/abs/physics/0601014 |
| DOI | 10.1088/0305-4470/39/42/009 |
| Journal | J.Phys.A39:13337-13353,2006; J.Phys.A39:13337-13354,2006 |
Abstract
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 Poincar\'{e} group of spin $j$ is obtained in the form: Classical fields and their conjugate momenta satisfy fundamental field-theoretic Poisson bracket relations for 2$j$ even, and fundamental Poisson antibracket relations for 2$j$ odd
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"abstract": "The spin-statistics connection is obtained for a simple formulation of a\nclassical field theory containing even and odd Grassmann variables. To that\nend, the construction of irreducible canonical realizations of the rotation\ngroup corresponding to general causal fields is reviewed. The connection is\nobtained by imposing local commutativity on the fields and exploiting the\nparity operation to exchange spatial coordinates in the scalar product of\nclassical field evaluated at one spatial location with the same field evaluated\nat a distinct location. The spin-statistics connection for irreducible\ncanonical realizations of the Poincar\\\u0027{e} group of spin $j$ is obtained in the\nform: Classical fields and their conjugate momenta satisfy fundamental\nfield-theoretic Poisson bracket relations for 2$j$ even, and fundamental\nPoisson antibracket relations for 2$j$ odd",
"arxiv_id": "physics/0601014",
"authors": [
"J. A. Morgan"
],
"categories": [
"physics.class-ph"
],
"doi": "10.1088/0305-4470/39/42/009",
"journal_ref": "J.Phys.A39:13337-13353,2006; J.Phys.A39:13337-13354,2006",
"title": "The spin-statistics connection in classical field theory",
"url": "https://arxiv.org/abs/physics/0601014"
},
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