Noncommutative Geometry, Quantum Fields and Motives
by Alain Connes, Matilde Marcolli
Publisher: American Mathematical Society 2007
ISBN/ASIN: 0821842102
ISBN-13: 9780821842102
Number of pages: 705
Description:
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.
Download or read it online for free here:
Download link
(6.4MB, PDF)
Similar books
Geometry in Physicsby Alexander Altland
Contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory); Manifolds (Basic structures, Tangent space); Lie groups (Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).
(7232 views)
The Geometrization of Physicsby Richard S. Palais - University of California at Irvine
The major goal of these notes is to develop an observation that not only can gauge fields of the Yang-Mills type be unified with the Einstein model of gravitation, but also that when this unification is made they are described by pure geometry.
(8104 views)
Differential Geometry in Physicsby Gabriel Lugo - University of North Carolina at Wilmington
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.
(12868 views)
Edinburgh Lectures on Geometry, Analysis and Physicsby Michael Atiyah - arXiv
These notes are based on a set of six lectures that the author gave in Edinburgh and they cover some topics in the interface between Geometry and Physics. They involve some unsolved problems and they may stimulate readers to investigate them.
(5153 views)