Starting from undergraduate level, this book systematically develops the basics of - Analysis on manifolds, Lie groups and G-manifolds (including equivariant dynamics) - Symplectic algebra and geometry, Hamiltonian systems, symmetries and reduction, - Integrable systems, Hamilton-Jacobi theory (including Morse families, the Maslov class and caustics). The first item is relevant for virtually all areas of mathematical physics, while the second item provides the basis of Hamiltonian mechanics. The last item introduces to important special areas. Necessary background knowledge on topology is...

This monograph presents in detail the reduction method for studying the unification of fundamental actions. The mathematical (differential geometrical) methods make extensive use of Lie Groups and the concept of homogeneous spaces. The main topic of the book is the dimensional reduction of pure Yang-Mills theories. A rather complete analysis of the structure of the scalar field potential is given and a general procedure for solving the equations of spontaneous compactification within Einstein-Yang-Mills systems is presented. The authors also discuss gravity and theories with fermions included...

Starting from an undergraduate level, this book systematically develops the basics of * Calculus on manifolds, vector bundles, vector fields and differential forms, * Lie groups and Lie group actions, * Linear symplectic algebra and symplectic geometry, * Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an...