Relativistic wavefunctions on the Poincare group

Abstract

The Biedenharn type relativistic wavefunctions are considered on the group manifold of the Poincaré group. It is shown that the wavefunctions can be factorized on the group manifold into translation group and Lorentz group parts. A Lagrangian formalism and field equations for such factorizations are given. Parametrizations of the functions obtained are studied in terms of a ten-parameter set of the Poincaré group. An explicit construction of the wavefunction for the spin 1/2 is given. A relation of the proposed description with the quantum field theory and harmonic analysis on the Poincaré group is discussed.

11 pages

References in corpus (4)

• Higher-Spin Gauge Theories in Four, Three and Two Dimensions
• A Universal Model of D=4 Spinning Particle
• Geometro-Stochastically Quantized Fields with Internal Spin Variables
• Free Quantum Fields on the Poincare' Group

Cited by in corpus (6)

• Spinor Structure and Internal Symmetries
• CPT groups of higher spin fields
• General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains
• Spherical functions on the de Sitter group
• Relativistic Spherical Functions on the Lorentz Group
• Group averaging for de Sitter free fields in terms of hyperspherical functions