Research Catalog

Title

The Skyrme model : fundamentals, methods, applications / V.G. Makhankov, Y.P. Rybakov, V.I. Sanyuk.

Author

Makhanʹkov, V. G.

Publication

Berlin ; New York : Springer-Verlag, [1993], ©1993.

Items in the Library & Off-site

Holdings

Details

Additional Authors

• Rybakov, Y. P. (Yurii P.), 1939-
• Sanyuk, V. I. (Valerii I.), 1950-

Description

xviii, 265 pages : illustrations; 24 cm.

Series Statement

Springer series in nuclear and particle physics

Uniform Title

Springer series in nuclear and particle physics.

Subject

• Skyrme model

Bibliography (note)

• Includes bibliographical references (p. [243]-260) and index.

Contents

• 1. The Evolution of Skyrme's Approach. 1.1. The "Mesonic Fluid" Model. 1.2. The Chiral Modification. 1.3. The Two-Dimensional Simplified (sine-Gordon) Model. 1.4. The Baryon Model - Topological Skyrmions. 1.5. Skyrme's Results and Conjectures -- 2. Elements of Field Theory with Topological Charges. 2.1. Geometric Viewpoint on the Classical Field Theory. 2.2. The Topological Classification of Solutions. 2.3. Isham's Construction of Topological Charges. 2.4. Guiding Principles in the Choice of Model Lagrangians -- 3. Topological Stability. 3.1. Some General Remarks. 3.2. The Hobart-Derrick Theorem. 3.3. Soliton Stability and the Second Variation Structure of the Lyapunov Functional. 3.4. The Topological Stability of Skyrmions -- 4. The Principle of Symmetric Criticality. 4.1. Some Auxiliary Information. 4.2. The Symmetry Group of the Skyrme Energy Functional. 4.3. The Coleman-Palais Theorem. 4.4. The Structure of Invariant Fields (Ansatze) -- 5. Absolute Minimum of the Energy Functional.
• 5.1. Method of Extending the Phase Space. 5.2. The Spherical Rearrangement Method. 5.3. Skyrmion as the Absolute Minimizer of the Energy -- 6. The Existence of Skyrmions. 6.1. The Field Equations for Skyrmions. 6.2. The Direct Method in the Calculus of Variations. 6.3. An Outline of the Proof of the Skyrmion Existence -- 7. Multi-Baryon and Rotating Skyrmion States. 7.1. The Problem of Bound States and Interaction Among Skyrmions. 7.2. Minima of the Energy Functional in Higher Homotopy Classes. 7.3. The Rotating Skyrmion -- 8. Quantization of Skyrmions. 8.1. Bogolubov's Method of Collective Coordinates. 8.2. Canonical Quantization of Skyrmions. 8.3. The "Non-Rigid" Quantization of Skyrmions -- 9. The Skyrme Model and QCD. 9.1. Express Review of the QCD Present Status. 9.2. 1/N-Expansion. 9.3. Effective Meson Theory from QCD -- 10. Skyrmion as a Fermion. 10.1. The Finkelstein's Double-Valued Functionals. 10.2. The Charge-Monopole Multi-valued Action.
• 10.3. The Wess-Zumino Term and Witten's Realization of Skyrme's Suggestion -- 11. Quantized SU(3) Skyrmions and Their Interactions. 11.1. The SU(3) Generalized Lagrangian in Terms of Collective Coordinates. 11.2. Quantization in the Presence of the Wess-Zumino Term. 11.3. Skyrmions' Interactions: Nuclear Forces and Nuclear Matter -- A. Chiral Symmetry. A.1. Algebraic Aspects of Chiral Symmetry. A.2. Geometric Aspects of Chiral Symmetry -- B. A Concise Account of Algebraic Topology. B.1. Smooth Manifolds. B.2. Tangent Spaces, Vector Fields and Lie Algebras. B.3. Differential Forms. B.4. Integration on Manifolds and De Rham Co-Homologies. B.5. Fundamental Groups, Homotopy Groups and Some Other Topological Invariants -- C. Methods of Reduction. C.1. Reduction to Static Field Configurations. C.2. Reduction to G-Invariant Fields. C.3. Spherical Rearrangement Technique: An Illustration -- D. Proofs of Stability and Existence Theorems. D.1. Proof of Generalized Hobart-Derrick Theorem.
• D.2. Existence of the Axially-Symmetric Solutions. D.3. Existence of a Nonsingular Matrix -- E. Finkelstein-Williams' Spinor Structures.

ISBN

• 3540549056 (Berlin : acid-free paper)
• 0387549056 (New York : acid-free paper)

LCCN

92028266

OCLC

• 26503977
• ocm26503977

Owning Institutions

Columbia University Libraries