Exotic smoothness, noncommutative geometry, and particle physics
نویسندگان
چکیده
منابع مشابه
Exotic Smoothness and Physics
The essential role played by differentiable structures in physics is reviewed in light of recent mathematical discoveries that topologically trivial space-time models, especially the simplest one, R , possess a rich multiplicity of such structures, no two of which are diffeomorphic to each other and thus to the standard one. This means that physics has available to it a new panoply of structure...
متن کاملNoncommutative Geometry and Physics
The two existing theories which successfully encode our knowledge of space-time are : • General Relativity • The Standard Model General relativity describes space-time as far as large scales are concerned (cf. Figure 1 and [2] for many more suggestive thoughts and pictures) and is based on the geometric paradigm discovered by Riemann. It replaces the flat (pseudo) metric of Poincaré, Einstein, ...
متن کاملSome Aspects of Noncommutative Geometry and Physics
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 t...
متن کاملRemarks on Quantum Physics and Noncommutative Geometry
The quantum-event / prime ideal in a category/ noncommutative-point alternative to classical-event / commutative prime ideal/ point is suggested. Ideals in additive categories, prime spectra and representation of quivers are considered as mathematical tools appropriate to model quantum mechanics. The space-time framework is to be reconstructed from the spectrum of the path category of a quiver....
متن کاملThe Interface of Noncommutative Geometry and Physics
As a mathematical theory per se, noncommutative geometry (NCG) is by now well established. From the beginning, its progress has been crucially influenced by quantum physics: we briefly review this development in recent years. The Standard Model of fundamental interactions, with its central role for the Dirac operator, led to several formulations culminating in the concept of a real spectral tri...
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ژورنال
عنوان ژورنال: International Journal of Theoretical Physics
سال: 1996
ISSN: 0020-7748,1572-9575
DOI: 10.1007/bf02302227