E-grāmata: Skyrme Model: Fundamentals Methods Applications

I Fundamentals.-
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.- 1.3.1 The Idea of Topological Charge.- 1.3.2
The Abelian Bosonization or Fermi-Bose Correspondence.- 1.4 The Baryon Model
- Topological Skyrmions.- 1.4.1 The (3+1)-dimensional "Angular" Variables.-
1.4.2 The Topological Charge in the (3+1) Model.- 1.4.3. The Skyrme Model
Dynamics.- 1.5 Skyrme's Results and Conjectures.-
2. Elements of Field Theory
with Topological Charges.- 2.1 Geometric Viewpoint on the Classical Field
Theory.- 2.1.1 The Configuration Space.- 2.1.2 Homotopy as a Formalization of
Dynamical Evolution.- 2.2 The Topological Classification of Solutions.- 2.2.1
Homotopy Classes of the sine-Gordon Model.- 2.2.2 The Fundamental and Higher
Homotopy Groups.- 2.3 Isham's Construction of Topological Charges.- 2.3.1
Cohomology - Homotopy Relationship in Brief.- 2.3.2 Derivation of Topological
Charge in the Skyrme Model.- 2.4 Guiding Principles in the Choice of Model
Lagrangians.- 2.4.1 Chirally Invariant 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.- 3.3.1 The Lyapunov Stability of Solitons.- 3.3.2 The Generalized
Hobart-Derrick Theorem.- 3.3.3 The Q-stability of Solitons.- 3.4 The
Topological Stability of Skyrmions.- II Methods for the Study 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.- 7.1.1 The Invariant Fields in Higher
Homotopy Classes.- 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.- III Hadron
Physics Applications.-
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.- 9.3.1 The Low-energy QCD Attributes.- 9.3.2 The Topological Charge as
the Baryon Number.- 9.3.3 Effective Chiral Lagrangians 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.- 10.3.1 The Wess-Zumino Term in
Effective Chiral Lagrangian.- 10.3.2 Spin and Statistics of Skyrmions.-
11.
Quantized SU(3) Skyrmions and Their Interactions.- 11.1 The SU(Z) Generalized
Lagrangian in Terms of Collective Coordinates.- 11.1.1 The SU(3) Skyrme
"Collective" Lagrangian.- 11.1.2 The Wess-Zumino Term for Collective
Coordinates.- 11.1.3 The Symmetry Breaking Term.- 11.2 Quantization in the
Presence of the Wess-Zumino Term.- 11.2.1 Canonical Quantization.- 11.2.2
Symmetries, Constraint and Spectrum.- 11.2.3 Static Observables and Mass
Formulae.- 11.3 Skyrmions' Interactions: Nuclear Forces and Nuclear Matter.-
11.3.1 The Skyrmion-Skyrmion Interaction and Nuclear Forces.- 11.3.2 The
Meson-Baryon Interaction.- 11.3.3 The Skyrme Model and Nuclear Matter.-
Concluding Remarks.- IV Appendices.- 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.- References.