Traces in Number Theory, Geometry and Quantum Fields
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This book collects recent interactions between the fields of Global Analysis, Noncommutative Geometry, Number Theory and Dynamical Systems, organized around the common theme of traces, residues and zeta functions. It consists of a series of articles contributed by specialists in the various disciplines aimed at stressing interactions and different perspectives.
Traces and determinants arise in various guises in many areas of mathematics and mathematical physics: in regularization procedures in quantum fields theory, in the definition of correlation functions and partition functions, in index theory for manifolds and for noncommutative spaces, and in the study of dynamical systems, through zeta functions and zeta determinants, as well as in number theory in the study of zeta and L-functions. This volumes shows, through a series of concrete example, specific results as well as broad overviews, how similar methods based on traces and determinants arise in different perspectives in the fields of number theory, dynamical systems, noncommutative geometry, differential geometry and quantum field theory.