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Mathematical Association of America

Theodore Frankel

The geometry of physics : an introduction

Modern physics is taking more and more of a geometrical viewpoint - particle physics is full of terms like SU(2) and SO(3). Unfortunately, when students get to the point of needing to study such things in detail they are often 'thrown in at the deep end' - many books devote just a short space to the mathematics, so that they can get on to the physics more quickly. This means that students may struggle, or worse, end up with just a superficial idea of the subject. In 'The geometry of physics' Theodore Frankel goes for a more gentle approach. Rather than writing for graduate students, the book is aimed at undergraduates. It is steadily paced, and has plenty of diagrams, so that it can be worked through by the student, including those studying on their own.

The book is in three sections. The first part gives an introduction to differential geometry, looking at the properties of surfaces in three dimenstions. It then reformulates some of classical physics, such as electromagnetism, in the language of exterior differential forms. The second part goes further into tensor calculus, and demonstrates the application of this to General Relativity. The third part looks at quantum theory and particle physics, in particular the use of Lie groups in describing symmetries. It then shows how this has been used in the development of Yang-Mills theory.

Amazon.com info
Paperback 694 pages  
ISBN: 0521539277
Salesrank: 1711524
Weight:2.82 lbs
Published: 2003 Cambridge University Press
Marketplace:New from $101.22:Used from $39.95
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Amazon.co.uk info
Paperback 694 pages  
ISBN: 0521539277
Salesrank: 969612
Weight:2.82 lbs
Published: 2003 Cambridge University Press
Amazon price £40.00
Marketplace:New from £37.00:Used from £35.00
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Amazon.ca info
Paperback 694 pages  
ISBN: 0521539277
Salesrank: 2051306
Weight:2.82 lbs
Published: 2003 Cambridge University Press
Marketplace:New from CDN$ 162.62:Used from CDN$ 90.61
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Product Description
Theodore Frankel explains those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms essential to a better understanding of classical and modern physics and engineering. Key highlights of his new edition are the inclusion of three new appendices that cover symmetries, quarks, and meson masses; representations and hyperelastic bodies; and orbits and Morse-Bott Theory in compact Lie groups. Geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. First Edition Hb (1997): 0-521-38334-X First Edition Pb (1999): 0-521-38753-1