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Noncommutativity and Physics: A non-technical review
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting…
Entropy and the spectral action
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
We compute the information theoretic von Neumann entropy of the state associated to the fermionic second quantization of a spectral triple. We show that this entropy is given by th…
Geometry and the Quantum
Alain Connes
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the q…
Geometry and the Quantum: Basics
Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Fe…
Quanta of Geometry: Noncommutative Aspects
Ali H. Chamseddine, Alain Connes, Viatcheslav Mukhanov
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real sca…
Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification
Ali H. Chamseddine, Alain Connes, Walter D. van Suijlekom
The assumption that space-time is a noncommutative space formed as a product of a continuous four dimensional manifold times a finite space predicts, almost uniquely, the Standard…