Noncommutative spectral geometry, algebra doubling and the seeds of quantization

TL;DR

This paper explores how the two-sheeted space in noncommutative spectral geometry relates to dissipation and gauge structures, suggesting that algebra doubling inherently contains the origins of quantization.

Contribution

It demonstrates that algebra doubling in noncommutative spectral geometry encodes dissipation and gauge interactions, providing a classical foundation for quantization.

Findings

Algebra doubling relates to dissipation and gauge structure.

Dissipation plays a role in the emergence of quantization.

Noncommutative geometry's classical setup contains seeds of quantum behavior.

Abstract

A physical interpretation of the two-sheeted space, the most fundamental ingredient of noncommutative spectral geometry proposed by Connes as an approach to unification, is presented. It is shown that the doubling of the algebra is related to dissipation and to the gauge structure of the theory, the gauge field acting as a reservoir for the matter field. In a regime of completely deterministic dynamics, dissipation appears to play a key role in the quantization of the theory, according to 't Hooft's conjecture. It is thus argued that the noncommutative spectral geometry classical construction carries implicit in its feature of the doubling of the algebra the seeds of quantization.