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
14 - The Energy-Momentum Tensor
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
In this chapter we study the energy-momentum tensor. After defining it from the Lagrangian formalism, we consider conservation equations in general, and apply it to the energy–momentum tensor. We find an ambiguity in the definition of the energy–momentum tensor, we fix it by considering the symmetric tensor, and we find the interpretation of the tensor's components. The Belinfante tensor form is defined by coupling to gravity. Finally, we give as an example the electromagnetic field, for which we calculate the energy–momentum tensor.
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- Classical Field Theory , pp. 127 - 136Publisher: Cambridge University PressPrint publication year: 2019