Noncommutative Geometry of Gravity, Strings and Fields: A Panoramic Overview

Richard J. Szabo

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arXiv · 2511.22672

Noncommutative Geometry of Gravity, Strings and Fields: A Panoramic Overview

Richard J. Szabo

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Abstract

These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key mathematical approaches presented include operator algebras such as $C^*$-algebras, K-theory, spectral geometry, quantum groups, and deformation quantization. Physical application areas considered include string theory, quantum field theory, and the Standard Model, as well as certain condensed matter systems.

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Richard J. Szabo. 2025-11-27. Noncommutative Geometry of Gravity, Strings and Fields: A Panoramic Overview. https://arxiv.org/abs/2511.22672

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