The spin-statistics connection in classical field theory

Details The spin-statistics connection in classical field theory The spin-statistics connection in classical field theory

2006-01-03

arxiv.org/abs/physics/0601014v4

J.Phys.A39:13337-13353,2006; J.Phys.A39:13337-13354,2006

Physics

Classical Physics

27 pages. Typos and sign error corrected; minor revisions to text

Scientific paper

10.1088/0305-4470/39/42/009

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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