Geometry of Constrained Dynamical Systems

A lively, varied and topical presentation of this branch of theoretical physics.

John M. Charap (Edited by)

9780521482714, Cambridge University Press

Hardback, published 5 January 1995

352 pages
23.6 x 15.7 x 2.5 cm, 0.618 kg

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

Many of the fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The study of these constrained dynamical systems, in particular the problems encountered in 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 arose from a conference held during that symposium, and 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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]