DE SITTER SYMMETRIC FIELD THEORY .I. ONE-PARTICLE THEORY

The formal structure and the free-particle solutions of the field equations (Sμνpν + mγμ)ψ = p μψ, derived recently by the author [Nuovo Cimento 51A, 864 (1967)] for realizations of the inhomogeneous de Sitter group are discussed. The enveloping algebra of the group is developed, and the covariance of the field equations under the five-dimensional rotations C, P, and T is proved. Bhabha's representation of the matrices γμ is completed. Observables, expectation,values and the scalar product are defined, and classical conservation laws are derived. The field equations are derived from a variational principle for the usual Lagrangian density ψ̄(- iγμ∂μ + m)ψ under a certain restriction. The free-particle solutions of the field equations are obtained in the canonical and the extreme relativistic representations. The connections between the wavefunctions in these representations, and also in the Foldy-Wouthuysen representation, are derived.