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

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 i...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Sakellariadou, Mairi, Stabile, Antonio, Vitiello, Giuseppe
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 11.01.2013
Subjects:	Algebra Deformation Field theory Quantum field theory Quantum theory Seeds
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	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.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1301.2563