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
23 - Radiation of a Classical Scalar Field: The Heisenberg Model
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 consider radiation from a classical scalar field. Polynomial potentials and the DBI scalar model are analyzed. A source moving at ultra-relativistic speeds (v very close to c) gives a shock wave solution. The solutions for the free scalar, interacting scalar and DBI scalar are found. We sketch the Heisenberg model for the collision of two ultrarelativistic hadrons leading to scalar radiation. The field and radiated energy are calculated.
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- Information
- Classical Field Theory , pp. 209 - 216Publisher: Cambridge University PressPrint publication year: 2019