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MATHEMATICAL PERSPECTIVES ON THEORETICAL PHYSICS
A Journey from Black Holes to Superstrings
by Nirmala Prakash (Visiting Scientist, Massachusetts Institute of Technology, USA)
Table of Contents (64k)
Preface (51k)
Chapter 1: Complex Functions, Riemann Surfaces, and Two-Dimensional Conformal Field Theory (An Introduction)
Chapter 1.1: Complex Functions (357k)
Chapter 1.2: Complex Structures on a Manifold, Kahler Metric (267k)
Chapter 1.3: Riemann Surfaces (1,077k)
Chapter 1.4: The Two-Dimensional Conformal Field Theory (422k)
This book presents the basics of mathematics that are needed for learning the physics of today. It describes briefly the theories of groups and operators, finite- and infinite-dimensional algebras, concepts of symmetry and supersymmetry, and then delineates their relations to theories of relativity and black holes, classical and quantum physics, electroweak fields and Yang–Mills. It concludes with a chapter on (the complex theory of) strings and superstrings and their link to black holes — an idea that fascinates both the physicist and the mathematician.
Contents:
- Complex Functions, Riemann Surfaces and Two-Dimensional Conformal
Field Theory (an Introduction)
- Elements of Group Theory and Group Representations
- A Primer on Operators
- Basics of Algebras and Related Concepts
- Infinite-Dimensional Algebras
- The Role of Symmetry in Physics and Mathematics
- All That's Super — An Introduction
- Gravitation, Relativity and Black Holes
- Basics of Quantum Theory
- Theory of Yang–Mills and the Yang–Mills–Higgs Mechanism
- Strings and Superstrings (Elementary Aspects)
Readership: Upper level undergraduates, graduate students, lecturers and
researchers in theoretical physics, mathematical physics, quantum physics and astrophysics as well as Yang– Mills and superstring theory.
"A very serious and scholarly work which deserves ... the attention of the physics community."
Claude R Canizares
Associate Provost
Massachusetts Institute of Technology, Cambridge |
"There is no better book than that of Prakash. It serves as a bridge between research cognoscenti and the simpler folks who use mathematical physics."
Ulrich Gerlach
Ohio State University, Columbus |
"A comprehensive mathematical resource for the topics covered."
Mike Guidry
University of Tennessee, Knoxville |
"An encyclopaedic work which will serve as an excellent resource for physicists."
Kenneth A Ross
University of Oregon, Eugene |
"Invaluable source for references and exercises on a wide range of topics in mathematical physics."
Kamesh Wali
Syracuse University, New York |
"Its chapters are many and long, but the individual sections are short and well-constructed. The exercises are accessible and hints provided. I recommend the book."
Michael Berg
Loyola Marymont University, Los Angeles |
| 864pp |
Pub. date: Sept 2003 |
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