Skyrmions: A Theory Of Nuclei

Contents
Foreword
Preface
1. Introduction
2. Fields and Particles
	2.1 The Classical Notions of Particles and Fields
		2.1.1 Quantum theory
	2.2 Quantum Field Theory and the Standard Model
	2.3 Pions and Nucleons
	2.4 Nuclei and Isospin
	2.5 Effective Field Theory
	2.6 Skyrme’s Effective Field Theory
3. Lagrangians and Symmetries
	3.1 Finite-Dimensional Systems
	3.2 Symmetries and Conservation Laws
	3.3 Lagrangian Field Theory
	3.4 Noether’s Theorem in Field Theory
4. Skyrme Theory
	4.1 SU(2)
	4.2 The Skyrme Lagrangian and Field Equation
	4.3 Skyrme Field Topology
		4.3.1 Topological degree of a map
	4.4 Skyrme Field Energy
		4.4.1 Elastic strain formulation
	4.5 Hedgehog Skyrmions
	4.6 Visualising Skyrmions
	4.7 Asymptotic Interactions of Hedgehogs
	4.8 Adding a Pion Mass Term
5. Quantization of Skyrmions
	5.1 Quantization of Skyrme Fields
	5.2 Topology and Quantization
	5.3 Rigid-Body Quantization
	5.4 Quantized Hedgehog Skyrmion – Proton and Neutron
	5.5 Classical Interpretation of Quantized Skyrmion States
	5.6 The Need for Fermionic Quantization
6. Skyrmions with Higher B – Massless Pions
	6.1 Skyrmions with Baryon Numbers B ≤ 8
	6.2 The Rational Map Ansatz
	6.3 Symmetric Rational Maps
		6.3.1 Platonic symmetries
	6.4 Skyrmions from Rational Maps
	6.5 Skyrmions up to B = 22
	6.6 Rigorous Investigation of Skyrmions
	6.7 The Skyrmion Crystal
7. Rigid-Body Skyrmion Quantization
	7.1 Collective Coordinate Quantization
	7.2 Rational Maps and Finkelstein–Rubinstein Signs
	7.3 Parity of States
	7.4 The Quantized Toroidal B = 2 Skyrmion
	7.5 The Quantized B = 3 Skyrmion
	7.6 The B = 4 Skyrmion and the α-Particle
	7.7 B = 5 and B = 7
	7.8 Quantization of the B = 6 Skyrmion
8. Skyrmions with Higher B – Massive Pions
	8.1 Massive Pions
	8.2 The Double Rational Map Ansatz
	8.3 Skyrmions from B = 8 to B = 32
		8.3.1 B = 8
		8.3.2 B = 12
		8.3.3 B = 16
		8.3.4 B = 24 and B = 32
	8.4 Geometrical Construction of Rational Maps
		8.4.1 B = 24 to B = 31 solutions by corner cutting
	8.5 Rational Maps with Oh and Td Symmetry
	8.6 Skyrmions up to Baryon Number 256
	8.7 Summary
9. Quantized Skyrmions with Even B ≤ 12
	9.1 Masses, Charge Radii and Calibration
	9.2 B = 4
	9.3 B = 6
	9.4 B = 8
	9.5 B = 10
	9.6 B = 12
		9.6.1 Quantizing the D3h-symmetric Skyrmion
		9.6.2 Comparison with experimental data
		9.6.3 The chain Skyrmion and the Hoyle band
		9.6.4 Matter radii
10. Skyrmion Deformations and Vibrations
	10.1 The Need to Consider Vibrations
	10.2 The α-Particle and its Vibrational Excitations
	10.3 Deformations of the B = 7 Skyrmion
	10.4 B = 12 Skyrmion Deformations and Carbon-12
		10.4.1 A multiphonon model for Carbon-12
11. Modelling Oxygen-16
	11.1 Introduction
	11.2 The Vibrational E-Manifold
		11.2.1 The Hamiltonian and quantum states
	11.3 E-Manifold States
		11.3.1 E-phonons
		11.3.2 Rovibrational states
	11.4 Beyond E-Vibrations
	11.5 The Complete Oxygen-16 Energy Spectrum
12. Modelling Calcium-40
	12.1 Tetrahedral Structure of Calcium-40
	12.2 Rovibrational Bands
	12.3 Interpreting the Calcium-40 Spectrum
	12.4 Summary
13. Electromagnetic Transition Strengths
	13.1 B(E2) Transition Strengths in Skyrme Theory
		13.1.1 Beryllium-8
		13.1.2 Carbon-12 and the Hoyle state
		13.1.3 Oxygen-16
		13.1.4 Neon-20, Magnesium-24 and Sulphur-32
	13.2 Beryllium-12
	13.3 Further Transitions
	13.4 Summary
14. Variants of Skyrme Theory
	14.1 Adding a Sextic Term
		14.1.1 The lightly-bound Skyrme model
	14.2 The BPS Skyrme Model
	14.3 Including Heavier Mesons
		14.3.1 Skyrme model with ρ mesons
		14.3.2 Skyrme model with ω mesons
	14.4 The SU(3) Extension of Skyrme Theory
15. The Sakai–Sugimoto Model
	15.1 Skyrmions from Instantons
	15.2 An Expansion for 4-Dimensional Gauge Potentials
	15.3 Baryon Resonances in the Sakai–Sugimoto Model
Bibliography
Index
About the Author