Constrained Hamiltonian systems and their symmetries

Author: Li Ziping
Publisher:
Publish Date: 2001-09-10
Features: Numerous physical systems exhibit constraints among canonical variables when described in phase space. For example, systems described by singular Lagrange densities (including all gauge theories) fall into this category. Such systems are constrained Hamiltonian systems. Their fundamental theories hold a significant position in modern quantum field theory. This book primarily introduces the classical and quantum theories of constrained Hamiltonian systems, with a focus on their symmetries. It covers topics such as the Dirac theory of constrained systems, Dirac bracket quantization, Faddeev-Senjanovic path (functional) integral quantization, and BFV quantization based on BRST symmetry. Additionally, it explores the classical and quantum canonical symmetries of constrained Hamiltonian systems, the theory of quantum conservation laws, and provides in-depth analyses of Yang-Mills theory and Chern-Simons theory as examples. This book is suitable not only for senior undergraduate and graduate students in physics but also for researchers and professionals working in theoretical physics, mathematical physics, particle physics theory, condensed matter theory, as well as related fields such as mathematics and mechanics.