Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- 20 Kink Solutions in ϕ4 and Sine-Gordon, Domain Walls and Topology
- 21 The Skyrmion Scalar Field Solution and Topology
- 22 Field Theory Solitons for Condensed Matter: The XY and Rotor Model, Spins, Superconductivity, and the KT Transition
- 23 Radiation of a Classical Scalar Field: The Heisenberg Model
- 24 Derrick’s Theorem, Bogomolnyi Bound, theAbelian-Higgs System, andSymmetryBreaking
- 25 The Nielsen-Olesen Vortex, Topology and Applications
- 26 Non-Abelian Gauge Theory and the Yang–Mills Equation
- 27 The Dirac Monopole and Dirac Quantization
- 28 The ’t Hooft–Polyakov Monopole Solution and Topology
- 29 The BPST-’t Hooft Instanton Solution and Topology
- 30 General Topology and Reduction on an Ansatz
- 31 Other Soliton Types. Nontopological Solitons: Q-Balls; Unstable Solitons: Sphalerons
- 32 Moduli Space; Soliton Scattering in Moduli Space Approximation; Collective Coordinates
- Part III Other Spins or Statistics; General Relativity
- References
- Index
25 - The Nielsen-Olesen Vortex, Topology and Applications
from Part II - Solitons and Topology; Non-Abelian Theory
Published online by Cambridge University Press: 04 March 2019
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- Part II Solitons and Topology; Non-Abelian Theory
- 20 Kink Solutions in ϕ4 and Sine-Gordon, Domain Walls and Topology
- 21 The Skyrmion Scalar Field Solution and Topology
- 22 Field Theory Solitons for Condensed Matter: The XY and Rotor Model, Spins, Superconductivity, and the KT Transition
- 23 Radiation of a Classical Scalar Field: The Heisenberg Model
- 24 Derrick’s Theorem, Bogomolnyi Bound, theAbelian-Higgs System, andSymmetryBreaking
- 25 The Nielsen-Olesen Vortex, Topology and Applications
- 26 Non-Abelian Gauge Theory and the Yang–Mills Equation
- 27 The Dirac Monopole and Dirac Quantization
- 28 The ’t Hooft–Polyakov Monopole Solution and Topology
- 29 The BPST-’t Hooft Instanton Solution and Topology
- 30 General Topology and Reduction on an Ansatz
- 31 Other Soliton Types. Nontopological Solitons: Q-Balls; Unstable Solitons: Sphalerons
- 32 Moduli Space; Soliton Scattering in Moduli Space Approximation; Collective Coordinates
- Part III Other Spins or Statistics; General Relativity
- References
- Index
Summary
In this chapter, we consider the vortex of the Abelian–Higgs system, the Nielsen–Olesen vortex (or ANO vortex). We find the Bogomolnyi bound for the energy of the system in terms of a topological charge. For a certain relation between coupling, known as a BPS limit, we find that the bound is saturated by a configuration with topological charge, i.e., magnetic charge. In this limit, we find BPS equations, which are solved by a vortex ansatz, for a vortex solution.The properties of the solutionand its application to superconductivity are explored.
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- Classical Field Theory , pp. 226 - 235Publisher: Cambridge University PressPrint publication year: 2019