## Mathematical Aspects of Classical Field Theory: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held July 20-26, 1991, with Support from the National Science FoundationClassical field theory has undergone a renaissance in recent years. Symplectic techniques have yielded deep insights into its foundations, as has an improved understanding of the variational calculus. Further impetus for the study of classical fields has come from other areas, such as integrable systems, Poisson geometry, global analysis, and quantum theory. This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory, held in July 1991 at the University of Washington at Seattle. The conference brought together researchers in many of the main areas of classical field theory to present the latest ideas and results. The volume contains thirty refereed papers, both survey and research articles, and is designed to reflect the state of the art as well as chart the future course of the subject. The topics fall into four major categories: global analysis and relativity (cosmic censorship, initial value problem, quantum gravity), geometric methods (symplectic and Poisson structures, momentum mappings, Dirac constraint theory), BRST theory, and the calculus of variations (the variational bicomplex, higher order theories). Also included are related topics with a ``classical basis'', such as geometric quantization, integrable systems, symmetries, deformation theory, and geometric mechanics. |

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### Contents

1 | |

Construction of locallysymmetric Lagrangian field theories from variational identities | 27 |

Introduction to the variational bicomplex | 51 |

WessZumino terms extended algebras and anomalies in classical physics | 75 |

Scattering and complete integrability in four dimensions | 99 |

A candidate maximal torus in infinite dimensions | 117 |

Censorship null geodesics and strong visibility | 125 |

Quasilocal energy in general relativity | 129 |

Stressenergymomentum tensors and the BelinfanteRosenfeld formula | 367 |

On the use of auxiliary fields in classical mechanics and in field theory | 393 |

Progress on strong cosmic censorship | 403 |

Loop algebras and canonical quantum gravity | 419 |

Prequantum BRST cohomology | 439 |

Jacobian quasibialgebras and quasiPoisson Lie groups | 459 |

Deformations and quantum statistical mechanics | 491 |

Canonical and BRSTquantization of constrained systems | 503 |

The reduction of Einsteins vacuum equations on spacetimes with spacelike U1isometry groups | 143 |

Finiteness theorems in Riemannian geometry and lattice quantum gravity | 171 |

Bihamiltonian manifolds and Tfunction | 213 |

On uniqueness in the large of solutions of Einsteins equations Strong cosmic censorship | 235 |

Reduction of degenerate nonautonomous Lagrangians | 275 |

On exactness of the variational bicomplex | 307 |

Geometric quantization and localization of relativistic spin systems | 317 |

Riemannian maps between Riemannian manifolds | 331 |

Classical observables of Gauge theories from the multitemporal approach | 531 |

Variational problems on graded manifolds | 551 |

The regularity of variational problems | 573 |

Homological ghost approach to constrained Hamiltonian systems | 595 |

A deformation theory of selfdual Einstein spaces | 611 |

What are the rules of the game called BRST? | 625 |

The residual symmetry of conformal gravity | 635 |

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### Common terms and phrases

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