Hamiltonian Mechanics of Gauge Systems

The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Lev V. Prokhorov is a Leading Research Fellow at the V.A. Fock Institute of Physics at St. Petersburg State University and the acting head of the Laboratory of Quantum Networks. He is known for his work in the fields of effective Lagrangians, deep inelastic scattering at small transfer momenta, grand unification theory, path integrals, infrared, and collinear divergences. His current research focuses on emergence of quantum mechanics and the nature of physical space. Among other honors, he has received the V.A. Fock Prize from the Russian Academy of Sciences
Sergei V. Shabanov is an Associate Professor of Mathematics and Affiliate Professor of Physics at the University of Florida. Gainesville. His research focuses on gauge theories and the path integral formalism, including the topological defects in lattice gauge theories and applications of knot solitons to effective infrared Yang-Mills theories, along with nanophotonics and plasma physics. His achievements include receiving the V.A. Fock Prize from the Russian Academy of Sciences, and an Alexander von Humboldt research fellowship