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Look Inside Geometry of Constrained Dynamical Systems

Geometry of Constrained Dynamical Systems

$51.95 (C)

Part of Publications of the Newton Institute

  • Date Published: July 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521070065

$ 51.95 (C)

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About the Authors
  • 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.

    • An up-to-date survey of this 'hot topic' in an active field of research
    • Important papers reporting on new developments, as well as survey reports on continuing lines of research
    Read more

    Reviews & endorsements

    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

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    Product details

    • Date Published: July 2008
    • format: Paperback
    • isbn: 9780521070065
    • length: 352 pages
    • dimensions: 229 x 152 x 20 mm
    • weight: 0.52kg
    • availability: Available
  • Table of Contents

    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.

  • Editor

    John M. Charap, Queen Mary University of London

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