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Mathematical Aspects of Classical Field Theory
Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 20-26, 1991
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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 resear...
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.
Table of contents:
V. Aldaya, M. M. Navarro, and J. Navarro-Salas: Hidden symmetry in field theory; S. C. Anco: Construction of locally-symmetric Lagrangian field theories from variational identities; I. M. Anderson: Introduction to the variational bicomplex; J. A. de Azcarraga: Wess-Zumino terms, extended algebras, and anomalies in classical physics; J. C. Baez: Scattering and complete integrability in four dimensions; D. D. W. Bao and T. Stefan Ratiu: A candidate maximal torus in infinite dimensions; J. K. Beem and A. Krolak: Censorship, null geodesics, and strong visibility; J. D. Brown and J. M. York: Quasilocal energy in general relativity; J. Cameron and V. E. Moncrief: The reduction of Einstein's vacuum equations on spacetimes with spacelike U (I)-isometry groups; M. Carfora and A. Marzuoli: Finiteness theorems in Riemannian geometry and lattice quantum gravity; P. Casati, F. Magri, and M. Pedroni: Bihamiltonian manifolds and r-function; P. T. Chrusciel: On uniqueness in the large of solutions of Einstein's equations ("Strong cosmic censorship"); M. De Leon, M. J. Mello, and P. R. Rodriques: Reduction of degenerate nonautonomous Lagrangians; L. Dickey: On exactness of the variational bicomplex; C. Dduval and J. Elhadad: Geometric quantization and localization of relativistic spin systems; A. E. Fischer: Reimannian maps between Riemannian manifolds; M. J. Gotay and J. E. Marsden: Stress-energy-momentum tensors and the Belinfante-Rosenfeld formula; M. Henneaux: On the use of auxillary fields in classical mechanics and in field theory; J. Isenberg; Progress on strong cosmic censorship; C. J. Isham: Loop algebras and canonical quantum gravity; T. Klmura: Prequantum BRST cohomology; Y. Kosmann-Schwarzbach: Jacobian quasi-bialgebras and quasi-Poisson Lie groups; A. Lichnerowicz: Deformations and quantum statistical mechanics; R. Loll: Canonical and RBST-quantization of constrained systems; L. Lusanna: Classical observables of Guage theories from the multitemporal approach; J. Monterde and M. J. Masque: Variational problems on graded manifolds; D. J. Saunders: The regularity of variational problems; J. D. Stasheff: Homological (ghost) approach to constrained Hamiltonian systems; C. A. Torre: A deformation theory of self-dual Einstein spaces; G. M. Tuynman: What are the rules of the game called BRST?; J. T. Wheeler: SU(3) x U(1): the residual symmetry of conformal gravity.
This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory. 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.
Table of contents:
V. Aldaya, M. M. Navarro, and J. Navarro-Salas: Hidden symmetry in field theory; S. C. Anco: Construction of locally-symmetric Lagrangian field theories from variational identities; I. M. Anderson: Introduction to the variational bicomplex; J. A. de Azcarraga: Wess-Zumino terms, extended algebras, and anomalies in classical physics; J. C. Baez: Scattering and complete integrability in four dimensions; D. D. W. Bao and T. Stefan Ratiu: A candidate maximal torus in infinite dimensions; J. K. Beem and A. Krolak: Censorship, null geodesics, and strong visibility; J. D. Brown and J. M. York: Quasilocal energy in general relativity; J. Cameron and V. E. Moncrief: The reduction of Einstein's vacuum equations on spacetimes with spacelike U (I)-isometry groups; M. Carfora and A. Marzuoli: Finiteness theorems in Riemannian geometry and lattice quantum gravity; P. Casati, F. Magri, and M. Pedroni: Bihamiltonian manifolds and r-function; P. T. Chrusciel: On uniqueness in the large of solutions of Einstein's equations ("Strong cosmic censorship"); M. De Leon, M. J. Mello, and P. R. Rodriques: Reduction of degenerate nonautonomous Lagrangians; L. Dickey: On exactness of the variational bicomplex; C. Dduval and J. Elhadad: Geometric quantization and localization of relativistic spin systems; A. E. Fischer: Reimannian maps between Riemannian manifolds; M. J. Gotay and J. E. Marsden: Stress-energy-momentum tensors and the Belinfante-Rosenfeld formula; M. Henneaux: On the use of auxillary fields in classical mechanics and in field theory; J. Isenberg; Progress on strong cosmic censorship; C. J. Isham: Loop algebras and canonical quantum gravity; T. Klmura: Prequantum BRST cohomology; Y. Kosmann-Schwarzbach: Jacobian quasi-bialgebras and quasi-Poisson Lie groups; A. Lichnerowicz: Deformations and quantum statistical mechanics; R. Loll: Canonical and RBST-quantization of constrained systems; L. Lusanna: Classical observables of Guage theories from the multitemporal approach; J. Monterde and M. J. Masque: Variational problems on graded manifolds; D. J. Saunders: The regularity of variational problems; J. D. Stasheff: Homological (ghost) approach to constrained Hamiltonian systems; C. A. Torre: A deformation theory of self-dual Einstein spaces; G. M. Tuynman: What are the rules of the game called BRST?; J. T. Wheeler: SU(3) x U(1): the residual symmetry of conformal gravity.
This book contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Mathematical Aspects of Classical Field Theory. 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.