Hamiltonian Mechanics of Gauge Systems.

Cover; HAMILTONIAN MECHANICS OF GAUGE SYSTEMS; CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS; Title; Copyright; Contents; Preface; 1 Hamiltonian formalism; 1.1 Hamilton's principle of stationary action; 1.1.1 Poincaré equations; 1.1.2 The existence of a Lagrangian for a dynamical system; 1.2 Hamiltonian equations of motion; 1.3 The Poisson bracket; 1.4 Canonical transformations; 1.5 Generating functions of canonical transformations; 1.6 Symmetries and integrals of motion; 1.6.1 Noether's theorem; 1.6.2 Integrals of motion and symmetry groups; 1.7 Lagrangian formalism for Grassmann variables.

1.8 Hamiltonian formalism for Grassmann variables1.9 Hamiltonian dynamics on supermanifolds; 1.10 Canonical transformations on symplectic supermanifolds; 1.10.1 Hamilton-Jacobi theory; 1.11 Noether's theorem for systems on supermanifolds; 1.11.1 Supersymmetry; 1.12 Non-canonical transformations; 1.13 Examples of systems with non-canonical symplectic structures; 1.13.1 A particle with friction; 1.13.2 q-Oscillator; 1.14 Some generalizations of the Hamiltonian dynamics; 1.14.1 Nambu Mechanics; 1.14.2 Lie-Poisson symplectic structure; 1.14.3 Non-symplectic structures.

1.15 Hamiltonian mechanics. Recent developments2 Hamiltonian path integrals; 2.1 Introduction; 2.1.1 Preliminary remarks; 2.1.2 Quantization; 2.2 Hamiltonian path integrals in quantum mechanics; 2.2.1 Definition of the Hamiltonian path integral; 2.2.2 Lagrangian path integrals; 2.3 Non-standard terms and basic equivalence rules; 2.3.1 Non-standard terms; 2.3.2 Basic equivalence rules; 2.3.3 Basic integrals in curvilinear coordinates. Lagrangian basic equivalence rules; 2.4 Equivalence rules; 2.4.1 Hamiltonian equivalence rules; 2.4.2 Lagrangian equivalence rules.

2.5 Rules for changing the base point2.5.1 Ambiguities of the formal expression (2.8); 2.5.2 Rules for changing the base point; 2.6 Canonical transformations and Hamiltonian path integrals; 2.6.1 Preliminary remarks; 2.6.2 Change of variables in Lagrangian path integrals. Coordinates topologically equivalent to Cartesian coordinates; 2.6.3 Canonical and unitary transformations; 2.6.4 Canonical transformations of the Hamiltonian path integrals; 2.7 Problems with non-trivial boundary conditions; 2.7.1 A particle in an infinite well; 2.7.2 A particle in a disk.

2.7.3 General problems with zero boundary conditions2.7.4 A particle in the potential qk; 2.7.5 Topologically nontrivial coordinates; 2.8 Quantization by the path integral method; 2.8.1 Lagrangian formalism; 2.8.2 Hamiltonian formalism; 3 Dynamical systems with constraints; 3.1 Introduction; 3.1.1 Comparison of the Lagrange and d'Alambert methods for constrained dynamics; 3.2 A general analysis of dynamical systems with constraints; 3.2.1 The Hamiltonian formalism; 3.2.2 Examples of systems with constraints; 3.2.3 The Lagrangian formalism; 3.3 Physical variables in systems with constraints.

3.3.1 The extended group of gauge transformations.

An introduction to Hamiltonian mechanics of systems with gauge symmetry for graduate students and researchers in theoretical and mathematical physics.

Print version record.

Includes bibliographical references (pages 452-462) and index.

English.

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