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Fuzzy Physics and Matrix Geometry

  • Robert W. Carroll
Part of the Mathematics and Its Applications book series (MAIA, volume 554)

Abstract

There has been a lot of fuzzy mathematics around to which we make no reference whatsoever. We will deal with a more or less precise theory of fuzzy physics following [9, 11, 12, 16, 41, 44, 46, 45, 69, 51, 146, 137, 138, 139, 208, 232, 257, 281, 284, 285, 286, 287, 288, 289, 290, 282, 329, 333, 336, 338, 344, 345, 353, 354, 389, 393, 435, 447, 449, 484, 451, 452, 528, 569, 573, 586, 626, 631, 646, 648, 658, 669](see especially [670] which appeared after much of this chapter was first written - we have now included some material from this however along with more elementary examples in later remarks and sections). There are several approaches possible and we will begin with the fuzzy sphere. It is probably better to start with some early papers (e.g. [284, 290, 451, 452] along with [144]) rather than say [447] which is interlaced with classical ideas from differential geometry and becomes heavier reading. We will assume known many ideas from classical geometry (with suitable reminders) and will concentrate on the fuzzy or q-versions here. Subsequently we will sketch other fuzzy material (especially coherent states) and indicate connections to matrix models and large N behavior in string or M theory. We have tried to maintain a consistent notation but occasionally this changes to fit with other notation; there should be no problem since definitions are often repeated.

Keywords

Coherent State Dirac Operator Conformal Field Theory Star Product Noncommutative Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Robert W. Carroll
    • 1
  1. 1.Mathematics DepartmentUniversity of IllinoisUrbanaUSA

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