A dynamical system described by a singular Lagrangian is subject to some in- herent phase space constraints and is called a constrained canonical system （or con- strained Hamiltonian system）. Gauge field theories （for example， QED， QFD， QCD， Supergravity， Superstring） belong to this category. These theories now dominate particle physics. The theory of a constrained canonical system can also be applied to the theories of condensed matter and some other research area （for ex- ample， the quantum field theories of anyons）. The theories of a constrained canon- ical system play a fundamental role in modern field theories. The quantization of a constrained canonical system with a singular Lagrangian remains one of the key problems of quantum field theory and is being intensively discussed in the litera- ture. Symmetry is now a fundamental concept in modern physics. As it is well known， the discussion of symmetry properties of a system is usually based on the examination of the Lagranigan in configuration space. In quantum theory， the phase-space path integral is more fundamental than the configuration-space path integral， the latterprovides for a Hamiltonian quadratic in canonical momenta， whereas the former can be applied to an arbitrary Hamiltonian. Thus， the phase- space form of the path integral is a necessary precursor to the configuration-space form of the path integral. Therefore， the investigation of symmetry properties of a system in phase space has a basic sense in quantum theories， which can be applied to more general cases.
作者簡(jiǎn)介
暫缺《Symmetries in Constrainde Canonical Systems（影印版）》作者簡(jiǎn)介
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