Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows

Details Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows Spectral Functionals, Nonholonomic Dirac Operators, and Noncommutative Ricci Flows

2008-06-24

arxiv.org/abs/0806.3814v3

J.Math.Phys.50:073503,2009

Physics

Mathematical Physics

latex2e, 11pt, 40 pages, v3, version accepted for publication in JMP, modified following referee's recommendations, new affili

Scientific paper

10.1063/1.3157146

We formulate a noncommutative generalization of the Ricci flow theory in the framework of spectral action approach to noncommutative geometry. Grisha Perelman's functionals are generated as commutative versions of certain spectral functionals defined by nonholonomic Dirac operators and corresponding spectral triples. We derive the formulas for spectral averaged energy and entropy functionals and state the conditions when such values describe (non)holonomic Riemannian configurations.

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