Geometry of Classical Fields (Dover Books on Mathematics)

A canonical quantization approach to classical field theory, this text is suitable for advanced undergraduates and graduate students. It is addressed to mathematicians interested in theoretical physics as well as theoretical physicists who use differential geometric methods in their modelling.
The two-part treatment begins with an introduction to the elementary notions of differential geometry, the theory of Lie groups, and manifolds of maps. This overview prepares readers for the terminology used to describe globally defined fields in the second part. The introductory chapters mostly use a coordinate-free language, whereas the calculations in the later chapters employ a coordinate description, a method used somewhat more in applications to physics. Part II concerns a systematic development of a covariant Hamiltonian formulation of field theory, starting from the principle of stationary actions. Each chapter features an individual set of references, and the text concludes with an index and glossary of symbols.