Classical and quantum particles from nongeneric conformal orbits

TL;DR

This paper explicitly describes nongeneric conformal orbits of SO(4,2), constructs their Hamiltonian dynamics, and quantizes them, showing their unitary representations align with Mack's classification.

Contribution

It provides a covariant description and quantization of nongeneric conformal orbits, linking them to established representation theory.

Findings

Explicit covariant description of nongeneric orbits

Construction and quantization of Hamiltonian systems

Unitary representations match Mack's classification

Abstract

The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary representations of conformal group fit into the classification described by Mack (G. Mack, Comm. Math. Phys. 55 (1977),1).