Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Introduction
- Part I General Properties of Fields; Scalars and Gauge Fields
- 1 Short Review of Classical Mechanics
- 2 Symmetries, Groups, and Lie algebras; Representations
- 3 Examples: The Rotation Group and SU(2)
- 4 Review of Special Relativity: Lorentz Tensors
- 5 Lagrangeans and the Notion of Field; Electromagnetism as a Field Theory
- 6 Scalar Field Theory, Origins, and Applications
- 7 Nonrelativistic Examples:WaterWaves and Surface Growth
- 8 Classical Integrability: Continuum Limit of Discrete, Lattice, and Spin Systems
- 9 Poisson Brackets for Field Theory and Equations of Motion: Applications
- 10 Classical Perturbation Theory and Formal Solutions to the Equations of Motion
- 11 Representations of the Lorentz Group
- 12 Statistics, Symmetry, and the Spin-Statistics Theorem
- 13 Electromagnetism and the Maxwell Equation; Abelian Vector Fields; Proca Field
- 14 The Energy-Momentum Tensor
- 15 Motion of Charged Particles and ElectromagneticWaves; Maxwell Duality
- 16 The Hopfion Solution and the Hopf Map
- 17 Complex Scalar Field and Electric Current: Gauging a Global Symmetry
- 18 The Noether Theoremand Applications
- 19 Nonrelativistic and Relativistic Fluid Dynamics: Fluid Vortices and Knots
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- References
- Index
13 - Electromagnetism and the Maxwell Equation; Abelian Vector Fields; Proca Field
from Part I - General Properties of Fields; Scalars and Gauge Fields
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
- 1 Short Review of Classical Mechanics
- 2 Symmetries, Groups, and Lie algebras; Representations
- 3 Examples: The Rotation Group and SU(2)
- 4 Review of Special Relativity: Lorentz Tensors
- 5 Lagrangeans and the Notion of Field; Electromagnetism as a Field Theory
- 6 Scalar Field Theory, Origins, and Applications
- 7 Nonrelativistic Examples:WaterWaves and Surface Growth
- 8 Classical Integrability: Continuum Limit of Discrete, Lattice, and Spin Systems
- 9 Poisson Brackets for Field Theory and Equations of Motion: Applications
- 10 Classical Perturbation Theory and Formal Solutions to the Equations of Motion
- 11 Representations of the Lorentz Group
- 12 Statistics, Symmetry, and the Spin-Statistics Theorem
- 13 Electromagnetism and the Maxwell Equation; Abelian Vector Fields; Proca Field
- 14 The Energy-Momentum Tensor
- 15 Motion of Charged Particles and ElectromagneticWaves; Maxwell Duality
- 16 The Hopfion Solution and the Hopf Map
- 17 Complex Scalar Field and Electric Current: Gauging a Global Symmetry
- 18 The Noether Theoremand Applications
- 19 Nonrelativistic and Relativistic Fluid Dynamics: Fluid Vortices and Knots
- Part II Solitons and Topology; Non-Abelian Theory
- Part III Other Spins or Statistics; General Relativity
- References
- Index
Summary
We describe electromagnetism as an Abelian gauge theory (for the Abelian group U(1)). Then we describe it in the language of p-forms, after defining p-forms and their formalism in detail. General p-form fields in various dimensions are also defined. Finally, we consider the massive vector field, the Proca field.
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- Classical Field Theory , pp. 118 - 126Publisher: Cambridge University PressPrint publication year: 2019