Quantum statistical mechanics and class field Theory
Abstract
Description
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.
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)
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)