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
26 - Non-Abelian Gauge Theory and the Yang–Mills Equation
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
We define nonabelian gauge theory. We start by defining nonabelian gauge groups and their properties, then (minimal) coupling other fields to the gauge field, through a covariant derivative. The action and gauge invariance of the pure Yang-Mills theory is given, and the resulting Yang-Mills equation (equation of motion) is derived.
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- Classical Field Theory , pp. 236 - 243Publisher: Cambridge University PressPrint publication year: 2019