Spectral functionals, nonholonomic Dirac operators, and noncommutative Ricci flows

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3157146· OSTI ID:21294215

Vacaru, Sergiu I ^[1]

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1. Science Department, University 'Al. I. Cuza' Iasi, 54. Lascar Catargi street, Iasi, 700107 (Romania) and Fields Institute for Research in Mathematical Science, 222 College Street, 2nd Floor, Toronto M5T 3J1 (Canada)

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.

• OSTI ID: 21294215
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 7; Other Information: DOI: 10.1063/1.3157146; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATION RELATIONS
DIRAC EQUATION
DIRAC OPERATORS
ENTROPY
FIELD THEORIES
FUNCTIONALS
GEOMETRY