Classical field theory and the stress-energy tensor [E-Book] /

Classical field theory and the stress-energy tensor [E-Book] / Mark S. Swanson.

Classical Field Theory and the Stress-Energy Tensor (Second Edition) is an introduction to classical field theory and the mathematics required to formulate and analyze it.

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Full text
Swanson, Mark S., author
Second edition.
Bristol: IOP Publishing, 2022
1 online resource (various pagings)
englisch
9780750334556
9780750334549
10.1088/978-0-7503-3455-6
Field theory (Physics)



  • 1. Geometry and physics
  • 1.1. Manifolds
  • 1.2. Coordinate systems
  • 1.3. The Jacobian
  • 1.4. Contravariant and covariant quantities
  • 1.5. The summation convention
  • 1.6. Vectors and direction vectors
  • 1.7. Vector addition and the scalar product
  • 1.8. The metric tensor and distance in manifolds
  • 1.9. The metric tensor and raising and lowering indices
  • 1.10. General tensors and tensor densities
  • 1.11. Trajectories and tangent spaces
  • 1.12. The vector product
  • 1.13. The gradient
  • 1.14. The divergence, the Laplacian, and the curl
  • 1.15. Differential forms and the wedge product
  • 1.16. Differential forms and Stokes' theorem
  • 1.17. The Lie derivative
  • 2. Newtonian mechanics and functional methods
  • 2.1. Newton's second law
  • 2.2. Newtonian trajectories and tangent vectors
  • 2.3. Newton's first law and Galilean relativity
  • 2.4. Functionals and the calculus of variations
  • 2.5. The action approach to Newtonian mechanics
  • 3. Basic field theory
  • 3.1. The mechanical properties of a stretched string
  • 3.2. The stretched string as a field theory
  • 3.3. The Euler-Lagrange equation for the stretched string
  • 3.4. Solving the Euler-Lagrange equation
  • 3.5. Galilean relativity and wave solutions
  • 3.6. Momentum and energy in field theories
  • 3.7. The stress-energy tensor
  • 3.8. Static sources and Green's function techniques
  • 3.9. The catenary, the Beltrami identity, and constraints
  • 3.10. Functional derivatives and Poisson brackets
  • 4. Newtonian fluid dynamics
  • 4.1. Fluid flow from Newtonian physics
  • 4.2. The equation of continuity
  • 4.3. Viscosity
  • 4.4. The Navier-Stokes equation and the stress-energy tensor
  • 4.5. Basic solutions to the Navier-Stokes equation
  • 4.6. Homentropic flow
  • 4.7. The action formulation for homentropic flow
  • 4.8. The homentropic stress-energy tensor
  • 4.9. The symmetric fluid stress-energy tensor
  • 4.10. Fluctuations around solutions and stability
  • 4.11. Spherical sound waves, power, and the Doppler effect
  • 5. Galilean covariant complex fields
  • 5.1. The complex classical nonrelativistic field
  • 5.2. The Euler-Lagrange equation and its solutions
  • 5.3. Symmetries of the Lagrangian
  • 5.4. Galilean covariance
  • 5.5. Complex analysis and Cauchy's theorem
  • 5.6. Scattering and the Dirac delta potential
  • 5.7. Bose-Einstein condensation
  • 5.8. Condensate fluctuations
  • 5.9. Vortices and the healing length
  • 6. Basic special relativity
  • 6.1. Maxwell's equations
  • 6.2. The problem with electromagnetic waves
  • 6.3. Lorentz transformations
  • 6.4. Observational effects of special relativity
  • 6.5. The Minkowski metric and space-time
  • 6.6. Relativistic energy and momentum
  • 6.7. Proper velocity and accelerated motion
  • 6.8. Relativistic action in the presence of force
  • 6.9. Relativistic quantities
  • 7. Linear algebra and group theory
  • 7.1. Linear algebra and matrices
  • 7.2. Basic group theory
  • 7.3. SO (3,1) and the Lorentz group
  • 7.4. Spinor representations of the Lorentz group
  • 8. Scalar and spinor field theories
  • 8.1. Classical point particles
  • 8.2. Lorentz invariant actions
  • 8.3. Relativistic scalar field theory
  • 8.4. Classical scalar solutions and broken symmetry
  • 8.5. Relativistic spinor fields and quadratic actions
  • 8.6. Symmetry and conservation laws
  • 9. Classical relativistic electrodynamics
  • 9.1. Aspects of Maxwell's equations
  • 9.2. The Helmholtz decomposition and the Coulomb potential
  • 9.3. The field strength tensor
  • 9.4. Electromagnetic fields and the gauge field
  • 9.5. Gauge transformations and gauge conditions
  • 9.6. Natural units
  • 9.7. The gauge field action and minimal coupling
  • 9.8. Relativistic point charges and electromagnetic interactions
  • 9.9. The stress-energy tensor and electrodynamics
  • 9.10. Angular momentum for gauge and spinor fields
  • 9.11. Electromagnetic waves and spin
  • 9.12. The Proca field
  • 9.13. Green's functions and electromagnetic radiation
  • 9.14. The gauge field as a differential form
  • 9.15. Magnetic monopoles
  • 10. General relativity and gravitation
  • 10.1. The metric tensor and Einstein's principle of equivalence
  • 10.2. The affine connection and the covariant derivative
  • 10.3. The curvature tensor
  • 10.4. The connection and curvature in differential geometry
  • 10.5. Variational techniques in general relativity
  • 10.6. The generalized stress-energy tensor
  • 10.7. Einstein's field equation
  • 10.8. Vacuum solutions to Einstein's equation
  • 10.9. Kaluza-Klein theory
  • 10.10. Basic cosmology
  • 11. Yang-Mills fields and connections
  • 11.1. Unitary symmetry and isospin
  • 11.2. Nonabelian gauge fields
  • 11.3. The Yang-Mills stress-energy tensor and force equation
  • 11.4. Spontaneous breakdown of symmetry
  • 11.5. Aspects of classical solutions for Yang-Mills fields
  • 11.6. Yang-Mills fields, forms, and connections
  • 11.7. Spinor fields in general relativity
  • 11.8. Yang-Mills fields and the Gribov instability
  • 11.9. Classical string theory.