Description 
1 online resource (486 pages) 
Series 
Cambridge Monographs on Mathematical Physics 

Cambridge monographs on mathematical physics.

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 PoincarĂ© 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 

1.15 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 Nonstandard terms and basic equivalence rules; 2.3.1 Nonstandard 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 

1.8 Hamiltonian formalism for Grassmann variables1.9 Hamiltonian dynamics on supermanifolds; 1.10 Canonical transformations on symplectic supermanifolds; 1.10.1 HamiltonJacobi theory; 1.11 Noether's theorem for systems on supermanifolds; 1.11.1 Supersymmetry; 1.12 Noncanonical transformations; 1.13 Examples of systems with noncanonical symplectic structures; 1.13.1 A particle with friction; 1.13.2 qOscillator; 1.14 Some generalizations of the Hamiltonian dynamics; 1.14.1 Nambu Mechanics; 1.14.2 LiePoisson symplectic structure; 1.14.3 Nonsymplectic structures 

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 nontrivial 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 
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 452462) and index 
Notes 
English 

Print version record 
Subject 
Gauge invariance.


Hamiltonian systems.

Form 
Electronic book

Author 
Shabanov, Sergei V.

LC no. 
2012359977 
ISBN 
0511976208 (ebook) 

052189512X (hardback) 

1139185683 

1139190598 (electronic bk.) 

9780511976209 (ebook) 

1139187996 

9780521895125 (hardback) 

9781139185684 

9781139187992 

9781139190596 (electronic bk.) 
