arXiv:math/0702379 Abstract

arXiv:math/0702379 [math.NT]Abstract References Reviews Resources

Quantum statistical mechanics and class field Theory

Published 2007-02-13Version 1

We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be realized in terms of the structure of equilibrium states of a quantum statistical mechanical system.

Comments: Survey article. To appear in the proceedings of the summer school "Geometric and topological methods for quantum field theory", Villa de Leyva 2005. (AMS Contemporary Mathematics)

Categories: math.NT, math.OA

Subjects: 58B34, 11R37, 82B10, 11R56

Keywords: class field theory, quantum statistical mechanics, number field, quantum statistical mechanical system, results appear

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