Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory

TL;DR

This paper explores how Alain Connes' noncommutative spectral geometry, especially algebra doubling, relates to gauge theories, dissipation, and quantization, revealing a connection to deformed Hopf algebra structures in quantum field theory.

Contribution

It demonstrates that algebra doubling in noncommutative geometry corresponds to deformed Hopf algebra structures, linking geometric and algebraic aspects of quantum field theory.

Findings

Algebra doubling relates to gauge structure and dissipation.

The structure of algebra doubling mirrors deformed Hopf algebra in QFT.

Algebra doubling contains elements of quantization.

Abstract

We report the results obtained in the study of Alain Connes noncommutative spectral geometry construction focusing on its essential ingredient of the algebra doubling. We show that such a two-sheeted structure is related with the gauge structure of the theory, its dissipative character and carries in itself the seeds of quantization. From the algebraic point of view, the algebra doubling process has the same structure of the deformed Hops algebra structure which characterizes quantum field theory.