  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.
