Geometry of Constrained Dynamical Systems

by John M. Charap

Overview

Many fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The study of these constrained dynamical systems, and in particular the problems of formulating them as quantum systems, has many profound links with geometry. These links were explored in the Symposium on Geometry and Gravity held at the Newton Institute in 1994. This book, which arose from a conference held during that symposium, is a collection of papers devoted to problems such as Chern-Simons theory, sigma-models, gauge invariance and loop quantization, general relativity and the notion of time, and quantum gravity. They present a lively, varied and topical perspective on this important branch of theoretical physics from some of the leading authorities in the subject, and will be of value to theoretical physicists and mathematicians interested in the latest advances.

Product Details

ISBN-13:	9780521070065
Publisher:	Cambridge University Press
Publication date:	07/31/2008
Series:	Publications of the Newton Institute , #3
Pages:	352
Product dimensions:	5.91(w) x 9.06(h) x 0.79(d)

Table of Contents

Preface; The network; 1. The constraint algebra of higher dimensional Chern–Simons; 2. Non-relativistic Chern–Simons vortices from the constrained Hamiltonian formalism; 3. Classical solutions of gravitating Chern–Simons electrodynamics; 4. Exponentionally localised instantons in a hierachy of Higgs models; 5. Obstructions to gauging WZ terms: a symplectic curiosity; 6. Global aspects of symmetries in sigma models with torsion; 7. Canonical structure of the non-linear sigma model in a polynomial formulation; 8. A manifestly gauge-invariant approach to quantum theories of gauge fields; 9. On the Hamiltonian formulation of the higher dimensional Chern–Simons gravity; 10. An example of loop quantization; 11. Gauge fixing in constrained systems; 12. Light-cone formulation of gauge theories; 13. Hamiltonian constraints and Dirac observables; 14. Gauging kinematical and internal symmetry groups for extended systems; 15. On the harmonic interaction of three relativistic point particles; 16. Non-existence of static multi-black-hole solutions in 2+1 dimensions; 17. Spherically symmetric gravity and the notion of time in general relativity; 18. Canonical decomposition of Belinskii–Zakharov one-soliton; 19. Hamiltonian reduction and the R-matrix of the Calogero model; 20. Intrinsic approach to the Legendre transformation in super-mechanics; 21. Field-antifield description of the anomalous theories; 22.Transfer matrix quantization of general relativity, and the problem of time; 23. The W3-particle; 24. Pure geometric approach to singular Lagrangians with higher derivatives; 25. Dirac versus reduced phase space quantization; 26. Classical and quantum aspects of degenerate metric field; 27. BRST-antibracket cohomology in 2D conformal gravity; 28. Quantization of 2+1 gravity for g=1 and g=2; 29. Geometry and dynamics with time-dependent constraints; 30. Collective coordinates and BRST transformations, or Gauge theories without gauge fields; 31. Geometry of fermionic constraints in superstring theories; 32. BRST and new superstring states; 33. Generalized canonical quantization of gauge theories with polarized second-class constraints; 34. Radiation field on superspace.

Editorial Reviews

Review of the hardback: 'Overall the book is interesting, provides a snapshot of the research in this field and a useful reference tool, that can replace scattered searching through the literature in the journals.' C. Rovelli, Classical & Quantum Gravity

From the Publisher

The 35 papers explain how many of the fundamental theories of modern physics can be considered descriptions of dynamical systems subjected to constraints, and explore how formulating the problems as quantum systems reveals profound links with geometry. The topics include exponentially localized instantons in a hierarchy of Higgs models, an example of loop quantization, spherically symmetric gravity and the notion of time in general relativity, and classical and quantum aspects of degenerate metric fields. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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