Geometry of Nonlinear Field Theories

This book discusses the deep connection between gravitation and the nonlinear sigma model coupled to gauge fields in a new perspective. Interesting developments emerge. Some other new aspects are provided such as the constant use of infinite dimensional differential geometry, a powerful tool not only for making the theory more rigorous but also for a heuristic understanding of field theory. A systematic treatment of the topological properties of Yang-Mills theory, the nonlinear sigma model and gravity is also given. Being sufficiently pedagogical and self-contained, this book could also be used as a base for an interdisciplinary course at the graduate level.