General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

Abstract

A construction of relativistic wave equations on the homogeneous spaces of the Poincaré group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is shown that a direct product of Minkowski spacetime and two-dimensional complex sphere is the most suitable homogeneous space for the physical applications. The Lagrangian formalism and field equations on the Poincaré and Lorentz groups are considered. A boundary value problem for the relativistically invariant system is defined. General solutions of this problem are expressed via an expansion in hyperspherical functions defined on the complex two-sphere.

56 pages, LaTeX2e

References in corpus (5)

• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• Photon wave function
• Maxwell field on the Poincare group
• Free Quantum Fields on the Poincare' Group
• Relativistic wavefunctions on the Poincare group

Cited by in corpus (10)

• Spinor Structure and Internal Symmetries
• CPT groups of higher spin fields
• Field on Poincare group and quantum description of orientable objects
• Spherical functions on the de Sitter group
• Spinor Structure and Matter Spectrum
• Cyclic structures of Cliffordian supergroups and particle representations of Spin_+(1,3)
• Lorentz group and mass spectrum of elementary particles
• Spinor Structure and Modulo 8 Periodicity
• On algebraic structure of matter spectrum
• Convergence of quantum electrodynamics on the Poincare group