2025/11/27 by Szabo, Richard J.
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2511.22672
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.