Some Aspects of Noncommutative Geometry and Physics
نویسنده
چکیده
An introduction is given to some selected aspects of noncommutative geometry. Simple examples in this context are provided by finite sets and lattices. As an application, it is explained how the nonlinear Toda lattice and a discrete time version of it can be understood as generalized σ-models based on noncommutative geometries. In particular, in this way one achieves a simple understanding of the complete integrability of the Toda lattice. Furthermore, generalized metric structures on finite sets and lattices are briefly discussed.
منابع مشابه
ar X iv : h ep - t h / 00 12 14 5 v 3 2 9 Ju l 2 00 1 Introduction to M ( atrix ) theory and noncommutative geometry
Noncommutative geometry is based on an idea that an associative algebra can be regarded as " an algebra of functions on a noncommutative space ". The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang-Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was f...
متن کاملJa n 20 01 Introduction to M ( atrix ) theory and noncommutative geometry
Noncommutative geometry is based on an idea that an associative algebra can be regarded as " an algebra of functions on a noncommutative space ". The major contribution to noncommutative geometry was made by A. Connes, who, in particular, analyzed Yang-Mills theories on noncommutative spaces, using important notions that were introduced in his papers (connection, Chern character, etc). It was f...
متن کامل0 Introduction to M ( atrix ) theory and noncommutative geometry
We give a mostly self-contained review of some aspects of M(atrix) theory and noncommutative geometry. The topics include introduction to BFSS and IKKT matrix models, compactifications on noncommutative tori, a review of basic notions of noncommutative geometry with a detailed discussion of noncommutative tori, Morita equivalence and SO(d, d|Z)-duality, an elementary discussion of instantons an...
متن کاملSinglet scalar dark matter in noncommutative space
In this paper, we examine the singlet scalar dark matter annihilation to becoming the Standard Model particles in the non-commutative space. In the recent decades, many candidates of dark matter have been offered, but our information about the nature of dark matter is still limited. There are such particle candidates as scalar matetr, fermion, boson, gauge boson, etc.; however, they have nei...
متن کاملNoncommutative generalization of SU(n)-principal ber bundles: a review
This is an extended version of a communication made at the international conference Noncommutative Geometry and Physics held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to the ordinary ber bundle theory. The noncommutative algebra is the endomorphism algebra of a SU(n)-vector bundle, and its di erential calculus is based on its Lie...
متن کامل