Swanson, Mark S., 1947-
Classical field theory and the stress-energy tensor / Mark S. Swanson. - Second edition. - 1 online resource (various pagings) : illustrations. - [IOP release $release] IOP ebooks. [2022 collection] . - IOP (Series). Release 22. IOP ebooks. 2022 collection. .
"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 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.
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.
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.
9780750334556 9780750334549
10.1088/978-0-7503-3455-6 doi
Field theory (Physics)
Physics.
Classical physics.
QC173.7 / .S833 2022eb
530.14
Classical field theory and the stress-energy tensor / Mark S. Swanson. - Second edition. - 1 online resource (various pagings) : illustrations. - [IOP release $release] IOP ebooks. [2022 collection] . - IOP (Series). Release 22. IOP ebooks. 2022 collection. .
"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 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.
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.
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.
9780750334556 9780750334549
10.1088/978-0-7503-3455-6 doi
Field theory (Physics)
Physics.
Classical physics.
QC173.7 / .S833 2022eb
530.14