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

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.

11 pages. Invited talk in the Sixth International Workshop DICE2012, Castello Pasquini/Castiglioncello (Tuscany), September 17-21, 2012

References in corpus (8)

• The mathematical basis for deterministic quantum mechanics
• Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
• Constraining the Noncommutative Spectral Action via Astrophysical Observations
• Inflation in models with Conformally Coupled Scalar fields: An application to the Noncommutative Spectral Action
• Gravitational Waves in the Spectral Action of Noncommutative Geometry
• Noncommutative spectral geometry, algebra doubling and the seeds of quantization
• Noncommutative Geometry Spectral Action as a framework for unification: Introduction and phenomenological/cosmological consequences
• Noncommutative spectral geometry, dissipation and the origin of quantization