eBook ISBN:  9780821877234 
Product Code:  CONM/132.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $94.75 
eBook ISBN:  9780821877234 
Product Code:  CONM/132.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $94.75 

Book DetailsContemporary MathematicsVolume: 132; 1992; 644 ppMSC: Primary 58; 70; 83
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.
ReadershipAdvanced graduate students and researchers in differential geometry, relativity, or mathematical physics.

Table of Contents

Articles

Víctor Aldaya, José NavarroSalas and Miguel Navarro — Hidden symmetries in field theory [ MR 1188432 ]

Stephen C. Anco — Construction of locallysymmetric Lagrangian field theories from variational identities [ MR 1188433 ]

Ian M. Anderson — Introduction to the variational bicomplex [ MR 1188434 ]

J. A. de Azcárraga — WessZumino terms, extended algebras and anomalies in classical physics [ MR 1188435 ]

John C. Baez — Scattering and complete integrability in four dimensions [ MR 1188436 ]

David Bao and Tudor Ratiu — A candidate maximal torus in infinite dimensions [ MR 1188437 ]

John K. Beem and Andrzej Królak — Censorship, null geodesics and strong visibility [ MR 1188438 ]

J. David Brown and James W. York, Jr. — Quasilocal energy in general relativity [ MR 1188439 ]

John Cameron and Vincent Moncrief — The reduction of Einstein’s vacuum equations on spacetimes with spacelike ${\rm U}(1)$isometry groups [ MR 1188440 ]

M. Carfora and A. Marzuoli — Finiteness theorems in Riemannian geometry and lattice quantum gravity [ MR 1188441 ]

Paolo Casati, Franco Magri and Marco Pedroni — BiHamiltonian manifolds and $\tau $function [ MR 1188442 ]

Piotr T. Chruściel — On uniqueness in the large of solutions of Einstein’s equations (“strong cosmic censorship”) [ MR 1188443 ]

Manuel de León, Maria Hermínia Mello and Paulo R. Rodrigues — Reduction of degenerate nonautonomous Lagrangians [ MR 1188444 ]

L. A. Dickey — On exactness of the variational bicomplex [ MR 1188445 ]

C. Duval and J. Elhadad — Geometric quantization and localization of relativistic spin systems [ MR 1188446 ]

Arthur E. Fischer — Riemannian maps between Riemannian manifolds [ MR 1188447 ]

Mark J. Gotay and Jerrold E. Marsden — Stressenergymomentum tensors and the BelinfanteRosenfeld formula [ MR 1188448 ]

Marc Henneaux — On the use of auxiliary fields in classical mechanics and in field theory [ MR 1188449 ]

James Isenberg — Progress on strong cosmic censorship [ MR 1188450 ]

C. J. Isham — Loop algebras and canonical quantum gravity [ MR 1188451 ]

Takashi Kimura — Prequantum BRST cohomology [ MR 1188452 ]

Yvette KosmannSchwarzbach — Jacobian quasibialgebras and quasiPoisson Lie groups [ MR 1188453 ]

A. Lichnerowicz — Deformations and quantum statistical mechanics [ MR 1188454 ]

R. Loll — Canonical and BRSTquantization of constrained systems [ MR 1188455 ]

Luca Lusanna — Classical observables of gauge theories from the multitemporal approach [ MR 1188456 ]

J. Monterde and J. Muñoz Masqué — Variational problems on graded manifolds [ MR 1188457 ]

D. J. Saunders — The regularity of variational problems [ MR 1188458 ]

Jim Stasheff — Homological (ghost) approach to constrained Hamiltonian systems [ MR 1188459 ]

C. G. Torre — A deformation theory of selfdual Einstein spaces [ MR 1188460 ]

G. M. Tuynman — What are the rules of the game called BRST? [ MR 1188461 ]

James T. Wheeler — ${\rm SU}(3)\times {\rm SU}(2)\times {\rm U}(1)$: the residual symmetry of conformal gravity [ MR 1188462 ]


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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.
Advanced graduate students and researchers in differential geometry, relativity, or mathematical physics.

Articles

Víctor Aldaya, José NavarroSalas and Miguel Navarro — Hidden symmetries in field theory [ MR 1188432 ]

Stephen C. Anco — Construction of locallysymmetric Lagrangian field theories from variational identities [ MR 1188433 ]

Ian M. Anderson — Introduction to the variational bicomplex [ MR 1188434 ]

J. A. de Azcárraga — WessZumino terms, extended algebras and anomalies in classical physics [ MR 1188435 ]

John C. Baez — Scattering and complete integrability in four dimensions [ MR 1188436 ]

David Bao and Tudor Ratiu — A candidate maximal torus in infinite dimensions [ MR 1188437 ]

John K. Beem and Andrzej Królak — Censorship, null geodesics and strong visibility [ MR 1188438 ]

J. David Brown and James W. York, Jr. — Quasilocal energy in general relativity [ MR 1188439 ]

John Cameron and Vincent Moncrief — The reduction of Einstein’s vacuum equations on spacetimes with spacelike ${\rm U}(1)$isometry groups [ MR 1188440 ]

M. Carfora and A. Marzuoli — Finiteness theorems in Riemannian geometry and lattice quantum gravity [ MR 1188441 ]

Paolo Casati, Franco Magri and Marco Pedroni — BiHamiltonian manifolds and $\tau $function [ MR 1188442 ]

Piotr T. Chruściel — On uniqueness in the large of solutions of Einstein’s equations (“strong cosmic censorship”) [ MR 1188443 ]

Manuel de León, Maria Hermínia Mello and Paulo R. Rodrigues — Reduction of degenerate nonautonomous Lagrangians [ MR 1188444 ]

L. A. Dickey — On exactness of the variational bicomplex [ MR 1188445 ]

C. Duval and J. Elhadad — Geometric quantization and localization of relativistic spin systems [ MR 1188446 ]

Arthur E. Fischer — Riemannian maps between Riemannian manifolds [ MR 1188447 ]

Mark J. Gotay and Jerrold E. Marsden — Stressenergymomentum tensors and the BelinfanteRosenfeld formula [ MR 1188448 ]

Marc Henneaux — On the use of auxiliary fields in classical mechanics and in field theory [ MR 1188449 ]

James Isenberg — Progress on strong cosmic censorship [ MR 1188450 ]

C. J. Isham — Loop algebras and canonical quantum gravity [ MR 1188451 ]

Takashi Kimura — Prequantum BRST cohomology [ MR 1188452 ]

Yvette KosmannSchwarzbach — Jacobian quasibialgebras and quasiPoisson Lie groups [ MR 1188453 ]

A. Lichnerowicz — Deformations and quantum statistical mechanics [ MR 1188454 ]

R. Loll — Canonical and BRSTquantization of constrained systems [ MR 1188455 ]

Luca Lusanna — Classical observables of gauge theories from the multitemporal approach [ MR 1188456 ]

J. Monterde and J. Muñoz Masqué — Variational problems on graded manifolds [ MR 1188457 ]

D. J. Saunders — The regularity of variational problems [ MR 1188458 ]

Jim Stasheff — Homological (ghost) approach to constrained Hamiltonian systems [ MR 1188459 ]

C. G. Torre — A deformation theory of selfdual Einstein spaces [ MR 1188460 ]

G. M. Tuynman — What are the rules of the game called BRST? [ MR 1188461 ]

James T. Wheeler — ${\rm SU}(3)\times {\rm SU}(2)\times {\rm U}(1)$: the residual symmetry of conformal gravity [ MR 1188462 ]