| Description |
1 online resource (486 pages) |
| Series |
Cambridge Monographs on Mathematical Physics |
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Cambridge monographs on mathematical physics.
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| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
An introduction to Hamiltonian mechanics of systems with gauge symmetry for graduate students and researchers in theoretical and mathematical physics |
| Notes |
3.3.1 The extended group of gauge transformations |
| Bibliography |
Includes bibliographical references (pages 452-462) and index |
| Notes |
English |
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Print version record |
| Subject |
Gauge invariance.
|
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Hamiltonian systems.
|
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SCIENCE -- Waves & Wave Mechanics.
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Gauge invariance
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Hamiltonian systems
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| Genre/Form |
Electronic book
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| Form |
Electronic book
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| Author |
Shabanov, Sergei V
|
| ISBN |
9781139187992 |
|
1139187996 |
|
9780511976209 |
|
0511976208 |
|
9780521895125 |
|
052189512X |
|
9781139190596 |
|
1139190598 |
|
9781139185684 |
|
1139185683 |
|
1107219434 |
|
9781107219434 |
|
1139637770 |
|
9781139637770 |
|
1283383934 |
|
9781283383936 |
|
1139189298 |
|
9781139189293 |
|
9786613383938 |
|
6613383937 |
|
1139183370 |
|
9781139183376 |
|
