Canonical variables and analysis on so(n,2)

TL;DR

This paper explores Berezin's quantization of so(n,2) using generalized coherent states, identifying commuting observables and enabling explicit matrix calculations in a Fock-type representation.

Contribution

It provides a detailed analysis of Berezin's quantization approach for so(n,2), including the construction of commuting observables and the use of the Leibniz function for computations.

Findings

Identified a family of n commuting observables

Expressed basis for Fock-type representation space

Enabled explicit matrix calculations in a specific basis

Abstract

The approach of Berezin to the quantization of so(n,2) via generalized coherent states is considered in detail. A family of n commuting observables is found in which the basis for an associated Fock-type representation space is expressed. An interesting feature is that computations can be done by explicit matrix calculations in a particular basis. The basic technical tool is the Leibniz function, the inner product of coherent states.