Geometry of Constrained Dynamical Systems

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

• 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.