Geometry of constrained dynamical systems : proceedings of a conference held at the Isaac Newton Institute, Cambridge, 15-18 June 1994 ; ed. John M. Charap

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. Title 5 Copyright 6 Contents 7 The network 12 Preface 13 The constraint algebra of higherdimensional Chern-Simons theories 15 Nonrelativistic Chern-Simonsvortices from the constrainedHamiltonian formalism 19 Classical solutions of gravitatingChern-Simons electrodynamics 31 Exponentially localised instantonsin a hierarchy of Higgs models 37 Obstructions to gauging WZ terms:a symplectic curiosity 46 Global aspects of symmetries insigma models with torsion 52 Canonical structure of thenon-linear cr-model in apolynomial formulation 64 A manifestly gauge-invariantapproach to quantum theoriesof gauge fields 74 On the Hamiltonian formulation ofhigher dimensional Chern-Simonsgravity 101 An example of loop quantization 106 Gauge fixing in constrained systems 114 Light-cone formulation of gaugetheories 123 Hamiltonian constraints and Diracobservables 131 Gauging kinematical and internalsymmetry groups for extendedsystems 145 On the harmonic interaction of threerelativistic point particles 155 Non existence of static multi-blackhole solutions in 2+1 dimensions 164 Spherically Symmetric Gravity andthe Notion of Time in GeneralRelativity 172 Canonical decomposition ofBelinskii-Zakharov one-solitonsolutions 187 Hamiltonian reduction and thei?-matrix of the Calogero model 200 Intrinsic approach to the Legendretransformation in supermechanics 209 Field-antifield description ofanomalous theories 217 Transfer matrix quantization ofgeneral relativity, and theproblem of time 227 The W3-particle 234 Pure geometrical approach tosingular Lagrangians with higherderivatives 243 Dirac versus reduced phase spacequantization 253 Classical and quantum aspectsof degenerate metric fields 265 BRST-antibracket cohomology in2d conformal gravity 278 Quantisation of 2+1 gravityfor g = 1 and g = 2 291 Geometry and dynamics withtime-dependent constraints 299 Collective coordinates and BRSTtransformations orGauge theories without gauge fields 307 Geometry of fermionic constraintsin superstring theories 315 BRST and new superstring states 322 Generalized canonical quantizationof gauge theories with polarizedsecond-class constraints 330 Radiation field on superspace 339 Participants 346 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. Edited By John M. Charap. Includes Bibliographical References.

a Lively, Varied And Topical Presentation Of This Branch Of Theoretical Physics.

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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)

Many of the fundamental theories of modern physics can be considered as descriptions of dynamical systems subjected to constraints. The collected papers deal with problems such as; Chern-Simons theory, sigma-models, gauge invariance, general relativity and the notion of time, and quantum gravity.