Gauge mechanics / L. Mangiarotti, G. Sardanashvily.

Format:

Book

Author/Creator:

Mangiarotti, L.

Contributor:

Sardanashvili, G. A. (Gennadiĭ Aleksandrovich)

Language:

English

Subjects (All):

Gauge fields (Physics).

Manifolds (Mathematics).

Hamiltonian systems.

Lagrangian functions.

Relativistic mechanics.

Physical Description:

1 online resource (366 p.)

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c1998.

Language Note:

English

Summary:

This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed;

Contents:

Preface; Contents; Introduction; Chapter 1 Interlude: bundles, jets, connections; 1.1 Fibre bundles; 1.2 Multivector fields and differential forms; 1.3 Jet manifolds; 1.4 Connections; 1.5 Bundles with symmetries; 1.6 Composite fibre bundles; Chapter 2 Geometry of Poisson manifolds; 2.1 Jacobi structure; 2.2 Contact structure; 2.3 Poisson structure; 2.4 Symplectic structure; 2.5 Presymplectic structure; 2.6 Reduction of symplectic and Poisson structures; 2.7 Appendix. Poisson homology and cohomology; 2.8 Appendix. More brackets; 2.9 Appendix. Multisymplectic structures

Chapter 3 Hamiltonian systems3.1 Dynamic equations; 3.2 Poisson Hamiltonian systems; 3.3 Symplectic Hamiltonian systems; 3.4 Presymplectic Hamiltonian systems; 3.5 Dirac Hamiltonian systems; 3.6 Dirac constraint systems; 3.7 Hamiltonian systems with symmetries; 3.8 Appendix. Hamiltonian field theory; Chapter 4 Lagrangian time-dependent mechanics; 4.1 Fibre bundles over R; 4.2 Dynamic equations; 4.3 Dynamic connections; 4.4 Non-relativistic geodesic equations; 4.5 Reference frames; 4.6 Free motion equations; 4.7 Relative acceleration; 4.8 Lagrangian systems; 4.9 Newtonian systems

4.10 Holonomic constraints4.11 Non-holonomic constraints; 4.12 Lagrangian conservation laws; Chapter 5 Hamiltonian time-dependent mechanics; 5.1 Canonical Poisson structure; 5.2 Hamiltonian connections and Hamiltonian forms; 5.3 Canonical transformations; 5.4 The evolution equation; 5.5 Degenerate systems; 5.6 Quadratic degenerate systems; 5.7 Hamiltonian conservation laws; 5.8 Time-dependent systems with symmetries; 5.9 Systems with time-dependent parameters; 5.10 Unified Lagrangian and Hamiltonian formalism; 5.11 Vertical extension of Hamiltonian formalism

5.12 Appendix. Time-reparametrized mechanicsChapter 6 Relativistic mechanics; 6.1 Jets of submanifolds; 6.2 Relativistic velocity and momentum phase spaces; 6.3 Relativistic dynamics; 6.4 Relativistic geodesic equations; Appendix A Geometry of BRST mechanics; Appendix B On quantum time-dependent mechanics; Bibliography; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 332-346) and index.

ISBN:

9789812815958

9812815953