Main Geometry, topology, and physics Geometry, topology, and physics Mikio Nakahara Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories.
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Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations Cambridge U Press, Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc.
The book is written in the style of famous Landau-Lifshitz L-L multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics at least at the level of the L-L course.
No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.
Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics)
Geometry, Topology, And Physics [ Mikio Nakahara]
Geometry, Topology and Physics, Third Edition