## Geometry of Constrained Dynamical SystemsMany fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The study of these constrained dynamical systems, and in particular the problems of formulating them as quantum systems, has many profound links with geometry. These links were explored in the Symposium on Geometry and Gravity held at the Newton Institute in 1994. This book, which arose from a conference held during that symposium, is a collection of papers devoted to problems such as Chern-Simons theory, sigma-models, gauge invariance and loop quantization, general relativity and the notion of time, and quantum gravity. They present a lively, varied and topical perspective on this important branch of theoretical physics from some of the leading authorities in the subject, and will be of value to theoretical physicists and mathematicians interested in the latest advances. |

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### Contents

BRSTantibracket cohomology in 2d confornial gravity 264 | 1 |

Classical solutions of gravitating CliernSimons | 17 |

a symploctic curiosity | 32 |

Canonical structure of the nonlinear crmodel in a polynomial | 50 |

On the Hamiltonian formulation of higher dimensional Chern | 87 |

Gauge fixing in constrained systems | 100 |

Hamiltonian constraints and Dirac observables | 117 |

Gauging kinematical and internal symmetry groups | 131 |

Hamiltonian reduction and the J?matrix of | 186 |

Intrinsic approach to the Legendre transformation | 195 |

Transfer matrix quantization of general relativity and | 213 |

Pure geometrical approach to singular Lagrangians with | 229 |

Classical and quantum aspects of degenerate metric fields | 251 |

B3001 Leuven Belgium | 277 |

Collective coordinates and BRST transformations or Gauge | 293 |

BRST and new superstring states | 308 |

Sezione INFN di Firenze Largo E Fermi 2 Arcetri 50125 Firenze | 139 |

Non existence of static multiblackhole solutions in 2 + 1 | 150 |

Canonical decomposition of BelinskilZakharov onesoliton | 173 |

Radiation field 011 superspace | 325 |

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### Common terms and phrases

A/Qp Abelian action anomaly antifields arbitrary Ashtekar asymptotic black holes BRST bundle canonical center-of-mass Chern-Simons class constraints classical computation configuration conjugate constant constraint surface construct coordinates corresponding covariant curvature cylindrical measure degrees of freedom denote depend derivative diffeomorphism dimensional dimensions Dirac observables equations of motion Euclidean functions gauge field gauge fixing gauge group gauge invariant gauge theories gauge transformations given Grav Henneaux Higgs models Hilbert space holonomy homotopy integral kinematical Lagrangian Lett Lie algebra linear Lusanna manifold Math matrix metric momenta momentum non-linear non-trivial Nucl obtained operator parameter particle phase space Phys physical Poisson bracket problem quantization quantization method quantum field theory reduced phase space relativistic result satisfy scalar field scalar field theory sigma model solution space-time spinor structure supersymmetry supervector symmetry symplectic theorem topological vanishes variables vector field Wilson loop Yang-Mills theory zero