Supersymmetric quantum theory, non-commutative geometry, and gravitation. Lecture Notes Les Houches 1995

Details Supersymmetric quantum theory, non-commutative geometry, and gravitation. Lecture Notes Les Houches 1995 Supersymmetric quantum theory, non-commutative geometry, and gravitation. Lecture Notes Les Houches 1995

1997-06-18

arxiv.org/abs/hep-th/9706132v1

Physics

High Energy Physics

High Energy Physics - Theory

143 pages, LaTeX file + 3 eps-figures

Scientific paper

This is an expanded version of the notes to a course taught by the first author at the 1995 Les Houches Summer School. Constraints on a tentative reconciliation of quantum theory and general relativity are reviewed. It is explained what supersymmetric quantum theory teaches us about differential topology and geometry. Non-commutative differential topology and geometry are developed in some detail. As an example, the non-commutative torus is studied. An introduction to string theory and $M$(atrix) models is provided, and it is outlined how tools of non-commutative geometry can be used to explore the geometry of string theory and conformal field theory.

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