Applications of contact geometry and topology in physics / Arkady L Kholodenko.

Format:

Book

Author/Creator:

Kholodenko, Arkady Leonidovich, 1948-

Series:

Gale eBooks

Language:

English

Subjects (All):

Geometry.

Topology.

Mathematical physics.

Physical Description:

1 online resource (xiv, 475 pages) : illustrations

Place of Publication:

Hackensack, N.J. : World Scientific, 2013.

Language Note:

English

Summary:

Although contact geometry and topology is briefly discussed in V I Arnol'd's book ""Mathematical Methods of Classical Mechanics ""(Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges ""An Introduction to Contact Topology"" (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph ""Contact Geometry and Nonlinear Differential Equations"" (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of

Contents:

Preface; Contents; Chapter 1. Motivation and Background; 1.1 General Information; 1.2 Fluid Mechanics Formulation of Hamiltonian and Jacobian Mechanics. Emergence of the Force-Free Fields; 1.3 Some Basic Facts about the Force-Free Fields; Chapter 2. From Ideal Magnetohydrodynamics to String and Knot Theory; 2.1 General Information; 2.2 The Gillbarg Problem and the Theory of Foliations; 2.3 From String-Theoretic Lund-Regge Equation to Landau-Lifshitz Equation for the Vortex Filament; 2.4 Foliations of R3 by the Maxwellian Surfaces

2.5 The Maxwellian Tori and the Torus Knots Associated with ThemChapter 3. All About and Around Woltjer's Theorem; 3.1 General Information; 3.2 Equilibria in Liquid Crystals and the Faddeev-Skyrme Model for Pure Yang-Mills Fields; 3.3 Refinements of Woltjer's Theorem. Implications for Magnetohydrodynamics, Superconductivity and Liquid Crystals; 3.4 Proca's Massive Electrodynamics and Stueckelberg's Trick; 3.5 New Interpretation of the Dirac Monopole and its Use in the Problem of Quark Confinement; Chapter 4. Topologically Massive Gauge Theories and the Force-Free Fields

Chapter 5. Contact Geometry and Physics5.1 General Information; 5.2 Some Basic Facts about Contact Geometry and Topology; 5.3 Contact Geometry of Thermodynamics; 5.4 Contact and Symplectic Geometry and Liquid Crystals; 5.5 Force-Free (Beltrami) Fields and Contact Geometry and Topology of Hydrodynamics and Electromagnetism; 5.6 Many Facets of the Abelian Chern-Simons Functional and Their Relation to Monopoles, Dyons and the Faddeev-Skyrme Model; 5.6.1 General Information; 5.6.2 From Instantons to Monopoles; 5.6.3 Topology and the Non-Abelian Monopoles

5.6.4 Hydrodynamics and the Faddeev-Skyrme model5.6.5 Helicity and Monopoles; 5.6.6 Some Comments on Dyons and Their Classical Analogs; Chapter 6. Sub-Riemannian Geometry, Heisenberg Manifolds and Quantum Mechanics of Landau Levels; 6.1 Motivation; 6.2 The Benchmark Example; 6.3 Basics of Sub-Riemannian Geometry; 6.4 Glimpses of Quantum Mechanics; 6.5 Fiber Bundle Reformulation of Sub-Riemannian Geometry and Classical-Quantum Correspondence. Connection with Dirac Monopoles; Chapter 7. Abrikosov Lattices, TGB Phases in Liquid Crystals and Heisenberg Group

Chapter 8. Sub-Riemannian Geometry, Spin Dynamics and Quantum-Classical Optimal Control8.1 General Information; 8.2 Quantum Computers Paradigm and Dynamics of 2-Level Quantum Systems; 8.2.1 What is Quantum Computation and Quantum Computer?; 8.2.2 Connecting Quantum 2-Level Systems with Classical Reality by Using the Hopf Map; 8.2.3 Some Mathematical Facts about the Rigid Body Rotations and Their Applications to Physical Problems; 8.2.4 Poinsot versus Euler and Kirchhoff; 8.2.5 Two-Level Quantum Systems. List of Applications; 8.2.6 Contact Geometry on S3 and Optimal Control of 2-Level Systems

8.2.7 Dirac Quantization of Dynamical Systems with Constraints and Contact Geometry

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789814412094

9814412090

OCLC:

847526798