Classical field theory and the stress-energy tensor /

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"Version: 20220401"--Title page verso.Includes bibliographical references.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 derivative2. 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 mechanics3. 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 brackets4. 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 effect5. 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 length6. 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 quantities7. 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 group8. 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 laws9. 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 monopoles10. 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 cosmology11. 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.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.Advanced undergraduate and graduate level physics courses.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Mark Swanson is currently Emeritus Professor of Physics at the University of Connecticut and lives in Monroe, Connecticut.Title from PDF title page (viewed on May 8, 2022).

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Publisher

: .,

Collation

1 online resource (various pagings) :illustrations.

Language

English

ISBN/ISSN

9780750334556

Classification

530.14

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Edition

Second edition.

Subject(s)

Physics.
Field theory (Physics)
Classical physics.

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Statement of Responsibility

Mark S. Swanson.

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