Description of Particles in Scalar Hyperplane-Dependent Field Theory. I. The General Formalism

Abstract

The concept of scalar hyperplane-dependent fields is defined on the basis of the author's earlier treatments of the position operators for relativistic particles. Such fields are a special case of fields over homogeneous spaces of the Ponincar\'e group and are related to infinite families of integer spin particles with spin-dependent mass spectra. The intrinsic parity of the particles and degeneracy in the mass spectrum is examined. The Lagrangian formalism, including Noether's theorem, is developed and explored. It is shown that the existence of a Lagrangian formalism yields a normalization condition that is incompatible with the existence of space-like solutions. All is in preparation for the sequel to this paper which considers a specific model with Bose statistics and nondegenerate mass spectrum.