On conformal reflections in compactified phase space

TL;DR

This paper discusses the extension of conformal compactification of space-time and momentum space, proposing a unified compact phase space with potential implications for classical and quantum physics.

Contribution

It introduces new arguments supporting the conjecture that both space-time and momentum can be conformally compactified into a unified phase space.

Findings

Support for conformal compactification of space-time and momentum

Proposal of a convolution between space-time and momentum space

Potential implications for classical and quantum physics

Abstract

Some results from arguments of research dealt with R. Raczka are exposed and extended. In particular new arguments are brought in favor of the conjecture, formulated with him, that both space-time and momentum may be conformally compactified, building up a compact phase space of automorphism for the conformal group, where conformal reflections determine a convolution between space-time and momentum space which may have consequences of interest for both classical and quantum physics.