MATHEMATICAL ASPECTS OF CLASSICAL FIELD THEORY
Proceedings of the Joint AMS/IMS/SIAM
Summer Research Conference, Seattle, 1991.
Edited by: Mark J. Gotay, Jerrold E. Marsden, and
Vincent Moncrief
Description
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.
Contents
- V. Aldaya, M. Navarro, and J. Navarro-Salas -- Hidden symmetries 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. Bao and T. 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. W. York -- Quasilocal energy in general relativity
- J. Cameron and V. E. Moncrief -- The reduction of Einstein's vacuum
equations on spacetimes with spacelike $U(1)$-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
$\tau$-function
- P. T. Chrusciel -- On uniqueness in the large of solutions of Einstein's
equations ("Strong cosmic censorship")
- M. De Leon, M. H. Mello, and P. R. Rodrigues -- Reduction of degenerate
nonautonomous Lagrangians
- L. Dickey -- On exactness of the variational bicomplex
- C. Duval 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 auxiliary 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. Kimura -- 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 BRST-quantization of constrained systems
- L. Lusanna -- Classical observables of Gauge theories from the multitemporal
approach
- J. Monterde and J. M. Masque -- Variational problems on graded manifolds
- D. J. Saunders -- The regularity of variational problems
- J. Stasheff -- Homological (ghost) approach to constrained Hamiltonian
systems
- C. G. Torre -- A deformation theory of self-dual Einstein spaces
- G. M. Tuynman -- What are the rules of the game called BRST?
- J. T. Wheeler -- $SU(3)\times SU(2)\times U(1)$ : The residual symmetry
of conformal gravity
Details:
- Publisher: American Mathematical Society
- Distributor: American Mathematical Society
- Series: Contemporary Mathematics, ISSN: 0271-4132
- Volume: 132
- Publication Year: 1992
- ISBN: 0-8218-5144-6
- Paging: 644 pp.
- Binding: Softcover