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Noncommutative geometry Noncommutative quantum field theory Noncommutative torus Compactification (physics) Noncommutative algebraic geometry Matrix (mathematics) Noncommutative standard model Tensor field Theoretical physics Physics Noncommutative torus Compactification (physics) Matrix (mathematics) Noncommutative standard model Tensor field Noncommutative torus Compactification (physics) Matrix (mathematics) Noncommutative standard model Tensor field Noncommutative torus Compactification (physics) Matrix (mathematics) Noncommutative standard model Tensor field Noncommutative torus Compactification (physics) Matrix (mathematics) Noncommutative standard model Tensor field Noncommutative torus Compactification (physics) Matrix (mathematics) Noncommutative standard model Tensor field
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Noncommutative Geometry

ISBN: 9780121858605 出版年：1995 页码：678 Connes, Alain Academic Press_RM

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We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory.

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