The Resource Applications of contact geometry and topology in physics, by Arkady L Kholodenko (Clemson University, USA)
Applications of contact geometry and topology in physics, by Arkady L Kholodenko (Clemson University, USA)
 Summary
 Although contact geometry and topology is briefly discussed in V I Arnold's book "Mathematical Methods of Classical Mechanics" (SpringerVerlag, 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 the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous LandauLifshitz (LL) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the LL course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the LL course some problems/exercises are formulated along the way and, again as in the LL course, these are always supplemented by either solutions or by hints (with exact references). Unlike the LL course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text
 Language
 eng
 Extent
 1 online resource
 Contents

 Ch. 1. Motivation and background. 1.1. General information. 1.2. Fluid mechanics formulation of Hamiltonian and Jacobian mechanics. Emergence of the forcefree fields. 1.3. Some basic facts about the forcefree fields
 ch. 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 stringtheoretic LundRegge equation to LandauLifshitz equation for the vortex filament. 2.4. Foliations of R[symbol] by the Maxwellian surfaces. 2.5. The Maxwellian tori and the torus knots associated with them
 ch. 3. All about and around Woltjer's theorem. 3.1. General information. 3.2. Equilibria in liquid crystals and the FaddeevSkyrme model for pure YangMills 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
 ch. 4. Topologically massive gauge theories and the forcefree fields
 ch. 5. Contact geometry and physics. 5.1. 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. Forcefree (Beltrami) fields and contact geometry and topology of hydrodynamics and electromagnetism. 5.6. Many facets of the Abelian ChernSimons functional and their relation to monopoles, dyons and the FaddeevSkyrme model
 ch. 6. SubRiemannian geometry, Heisenberg manifolds and quantum mechanics of Landau levels. 6.1. Motivation. 6.2. The benchmark example. 6.3. Basics of subRiemannian geometry. 6.4. Glimpses of quantum mechanics. 6.5. Fiber bundle reformulation of subRiemannian geometry and classicalquantum correspondence. Connection with Dirac monopoles
 ch. 7. Abrikosov lattices, TGB phases in liquid crystals and Heisenberg group
 ch. 8. SubRiemannian geometry, spin dynamics and quantumclassical optimal control. 8.1. General information. 8.2. Quantum computers paradigm and dynamics of 2level quantum systems. 8.3. Beyond the 2level quantum systems. 8.4. Semiflexible polymers and quantum computers
 ch. 9. From contact geometry to contact topology. 9.1. General information. 9.2. Mathematics and physics of the Cauchy problem in quantum mechanics: Viktor Maslov versus David Bohm. 9.3. From Maslov and Bohm to Bell and beyond. 9.4. Harmonious coexistence of classical and quantum mechanics: all about and around the DuistermaatHeckman formula. 9.5. Mathematics and physics of Weinstein's conjecture: from classical statistical mechanics to SeibergWitten monopoles. 9.6. Quantum money, Lagrangian, Legendrian and transverse knots and links and the associated grid diagrams. 9.7. Latest developments in contact geometry and topology. A guided tour with physics applications in the perspective
 Isbn
 9789814412094
 Label
 Applications of contact geometry and topology in physics
 Title
 Applications of contact geometry and topology in physics
 Statement of responsibility
 by Arkady L Kholodenko (Clemson University, USA)
 Language
 eng
 Summary
 Although contact geometry and topology is briefly discussed in V I Arnold's book "Mathematical Methods of Classical Mechanics" (SpringerVerlag, 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 the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous LandauLifshitz (LL) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the LL course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the LL course some problems/exercises are formulated along the way and, again as in the LL course, these are always supplemented by either solutions or by hints (with exact references). Unlike the LL course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text
 Cataloging source
 N$T
 Dewey number
 530.15/636
 Index
 index present
 LC call number
 QC20.7.G44
 LC item number
 K46 2013eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Label
 Applications of contact geometry and topology in physics, by Arkady L Kholodenko (Clemson University, USA)
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 http://library.link/vocab/branchCode

 net
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Ch. 1. Motivation and background. 1.1. General information. 1.2. Fluid mechanics formulation of Hamiltonian and Jacobian mechanics. Emergence of the forcefree fields. 1.3. Some basic facts about the forcefree fields  ch. 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 stringtheoretic LundRegge equation to LandauLifshitz equation for the vortex filament. 2.4. Foliations of R[symbol] by the Maxwellian surfaces. 2.5. The Maxwellian tori and the torus knots associated with them  ch. 3. All about and around Woltjer's theorem. 3.1. General information. 3.2. Equilibria in liquid crystals and the FaddeevSkyrme model for pure YangMills 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  ch. 4. Topologically massive gauge theories and the forcefree fields  ch. 5. Contact geometry and physics. 5.1. 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. Forcefree (Beltrami) fields and contact geometry and topology of hydrodynamics and electromagnetism. 5.6. Many facets of the Abelian ChernSimons functional and their relation to monopoles, dyons and the FaddeevSkyrme model  ch. 6. SubRiemannian geometry, Heisenberg manifolds and quantum mechanics of Landau levels. 6.1. Motivation. 6.2. The benchmark example. 6.3. Basics of subRiemannian geometry. 6.4. Glimpses of quantum mechanics. 6.5. Fiber bundle reformulation of subRiemannian geometry and classicalquantum correspondence. Connection with Dirac monopoles  ch. 7. Abrikosov lattices, TGB phases in liquid crystals and Heisenberg group  ch. 8. SubRiemannian geometry, spin dynamics and quantumclassical optimal control. 8.1. General information. 8.2. Quantum computers paradigm and dynamics of 2level quantum systems. 8.3. Beyond the 2level quantum systems. 8.4. Semiflexible polymers and quantum computers  ch. 9. From contact geometry to contact topology. 9.1. General information. 9.2. Mathematics and physics of the Cauchy problem in quantum mechanics: Viktor Maslov versus David Bohm. 9.3. From Maslov and Bohm to Bell and beyond. 9.4. Harmonious coexistence of classical and quantum mechanics: all about and around the DuistermaatHeckman formula. 9.5. Mathematics and physics of Weinstein's conjecture: from classical statistical mechanics to SeibergWitten monopoles. 9.6. Quantum money, Lagrangian, Legendrian and transverse knots and links and the associated grid diagrams. 9.7. Latest developments in contact geometry and topology. A guided tour with physics applications in the perspective
 Control code
 ocn847526798
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9789814412094
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Quality assurance targets
 not applicable
 http://library.link/vocab/recordID
 .b36169390
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)847526798
 acaebk9814412090
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