
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 YangMills theory.