Noncommutative Geometry, Quantum Fields and Motives
by Alain Connes, Matilde Marcolli
Publisher: American Mathematical Society 2007
Number of pages: 705
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools.
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by C. Nash - arXiv
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
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These lectures notes are an introduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists.
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