1999/03/30 by T. Krajewski, Krajewski, T.
Mathematics · Physics and Astronomy · #81E13 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:81E13
paper · pdf · doi:10.48550/arxiv.math-ph/9903047
Latex, 219 pages including 23 eps figures, the author's PhD thesis (in french)
arxiv created 1999/03/30 · arxiv updated 2009/11/30
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral triples, differential calculus or gauge theories on projective modules. Within this framework, The index theorem and cyclic homology are applied to the probe of topologically non trivial properties of Chern-Simons and Yang-Mills action functionals in dimension 3 and 4. Following earlier work on the standard model in noncommutative geometry, it also provides a general study of all Yang-Mills-Higgs models based on space-times structures which are the product of usual space-time by a discrete space, with emphasis on the physical properties of the resulting theories. Finally, the last part is devoted to the development of classical and quantum gauge theory on the noncommutative torus in any dimension. It includes a discussion of topological properties and symmetries of the action as well as its perturbative quantization.