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 Foundation

Front Cover
Classical 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

Hidden symmetries in field theory
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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