Description 
1 online resource (xi, 392 pages) 
Contents 
1. Dynamic equations. 1.1. Preliminary. Fibre bundles over R. 1.2. Autonomous dynamic equations. 1.3. Dynamic equations. 1.4. Dynamic connections. 1.5. Nonrelativistic geodesic equations. 1.6. Reference frames. 1.7. Free motion equations. 1.8. Relative acceleration. 1.9. Newtonian systems. 1.10. Integrals of motion  2. Lagrangian mechanics. 2.1. Lagrangian formalism on Q[symbol]R. 2.2. Cartan and HamiltonDe Donder equations. 2.3. Quadratic Lagrangians. 2.4. Lagrangian and Newtonian systems. 2.5. Lagrangian conservation laws. 2.6. Gauge symmetries  3. Hamiltonian mechanics. 3.1. Geometry of Poisson manifolds. 3.2. Autonomous Hamiltonian systems. 3.3. Hamiltonian formalism on Q[symbol]R. 3.4. Homogeneous Hamiltonian formalism. 3.5. Lagrangian form of Hamiltonian formalism. 3.6. Associated Lagrangian and Hamiltonian systems. 3.7. Quadratic Lagrangian and Hamiltonian systems. 3.8. Hamiltonian conservation laws. 3.9. Timereparametrized mechanics  4. Algebraic quantization. 4.1. GNS construction. 4.2. Automorphisms of quantum systems. 4.3. Banach and Hilbert manifolds. 4.4. Hilbert and C*algebra bundles. 4.5. Connections on Hilbert and C*algebra bundles. 4.6. Instantwise quantization  5. Geometric quantization. 5.1. Geometric quantization of symplectic manifolds. 5.2. Geometric quantization of a cotangent bundle. 5.3. Leafwise geometric quantization. 5.4. Quantization of nonrelativistic mechanics. 5.5. Quantization with respect to different reference frames  6. Constraint Hamiltonian systems. 6.1. Autonomous Hamiltonian systems with constraints. 6.2. Dirac constraints. 6.3. Timedependent constraints. 6.4. Lagrangian constraints. 6.5. Geometric quantization of constraint systems  7. Integrable Hamiltonian systems. 7.1. Partially integrable systems with noncompact invariant submanifolds. 7.2. KAM theorem for partially integrable systems. 7.3. Superintegrable systems with noncompact invariant submanifolds. 7.4. Globally superintegrable systems. 7.5. Superintegrable Hamiltonian systems. 7.6. Example. Global Kepler system. 7.7. Nonautonomous integrable systems. 7.8. Quantization of superintegrable systems  8. Jacobi fields. 8.1. The vertical extension of Lagrangian mechanics. 8.2. The vertical extension of Hamiltonian mechanics. 8.3. Jacobi fields of completely integrable systems  9. Mechanics with timedependent parameters. 9.1. Lagrangian mechanics with parameters. 9.2. Hamiltonian mechanics with parameters. 9.3. Quantum mechanics with classical parameters. 9.4. Berry geometric factor. 9.5. Nonadiabatic holonomy operator  10. Relativistic mechanics. 10.1. Jets of submanifolds. 10.2. Lagrangian relativistic mechanics. 10.3. Relativistic geodesic equations. 10.4. Hamiltonian relativistic mechanics. 10.5. Geometric quantization of relativistic mechanics 
Summary 
The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The present book provides the geometric formulation of nonautonomous mechanics in a general setting of timedependent coordinate and reference frame transformations. This formulation of mechanics as like as that of classical field theory lies in the framework of general theory of dynamic systems, and Lagrangian and Hamiltonian formalisms on fiber bundles. The reader will find a strict mathematical exposition of nonautonomous dynamic systems, Lagrangian and Hamiltonian nonrelativistic mechanics, relativistic mechanics, quantum nonautonomous mechanics, together with a number of advanced models  superintegrable systems, nonautonomous constrained systems and theory of Jacobi fields. It also contains information on mechanical systems with timedependent parameters, nonadiabatic Berry phase theory, instantwise quantization, and quantization relative to different reference frames 
Bibliography 
Includes bibliographical references (pages 369376) and index 
Notes 
Print version record 
Subject 
Geometry, Differential.


Mathematical physics.


Mechanics  Mathematics.


Quantum theory  Mathematics.

Form 
Electronic book

Author 
Magiaradze, L. G.


Sardanashvili, G. A. (Gennadiĭ Aleksandrovich)

LC no. 
2011280752 
ISBN 
9789814313728 (electronic bk.) 

9789814313735 (electronic bk.) 

9814313726 (electronic bk.) 

9814313734 (electronic bk.) 
