Hora?iu N?staseCambridge University Press, 3/14/2019EAN 9781108477017, ISBN10: 1108477011Hardcover, 480 pages, 25.3 x 19.2 x 2.6 cmLanguage: EnglishClassical field theory predicts how physical fields interact with matter, and is a logical precursor to quantum field theory. This introduction focuses purely on modern classical field theory, helping graduates and researchers build an understanding of classical field theory methods before embarking on future studies in quantum field theory. It describes various classical methods for fields with negligible quantum effects, for instance electromagnetism and gravitational fields. It focuses on solutions that take advantage of classical field theory methods as opposed to applications or geometric properties. Other fields covered includes fermionic fields, scalar fields and Chern–Simons fields. Methods such as symmetries, global and local methods, Noether theorem and energy momentum tensor are also discussed, as well as important solutions of the classical equations, in particular soliton solutions.PrefaceIntroduction1. Short review of classical mechanics2. Symmetries, groups and Lie algebras. Representations3. Examplesthe rotation group and SU(2)4. Review of special relativity. Lorentz tensors5. Lagrangeans and the notion of fieldelectromagnetism as a field theory6. Scalar field theory, origins and applications7. Nonrelativistic exampleswater waves, surface growth8. Classical integrability. Continuum limit of discrete, lattice and spin systems9. Poisson brackets for field theory and equations of motion. Applications10. Classical perturbation theory and formal solutions to the equations of motion11. Representations of the Lorentz group12. Statistics, symmetry, and the spin-statistics theorem13. Electromagnetism and the Maxwell equationAbelian vector fieldsProca field14. The energy-momentum tensor15. Motion of charged particles and electromagnetic wavesMaxwell duality16. The Hopfion solution and the Hopf map17. Complex scalar field and electric current. Gauging a global symmetry18. The Noether theorem and applications19. Nonrelativistic and relativistic fluid dynamics. Fluid vortices and knots20. Kink solutions in ø4 and sine-Gordon, domain walls and topology21. The Skyrmion scalar field solution and topology22. Field theory solitons for condensed matterthe XY and rotor model, spins, superconductivity and the KT transition23. Radiation of a classical scalar field. The Heisenberg model24. Derrick's theorem, Bogomolnyi bound, the Abelian–Higgs system and symmetry breaking25. The Nielsen–Olesen vortex, topology and applications26. Nonabelian gauge theory and the Yang–Mills equation27. The Dirac monopole and Dirac quantization28. The 't Hooft–Polyakov monopole solution and topology29. The BPST-'t Hooft instanton solution and topology30. General topology and reduction on an ansatz31. Other soliton types. Nontopological solitonsQ-ballsunstable solitonssphalerons32. Moduli spacesoliton scattering in moduli space approximationcollective coordinates33. Chern–Simons termsemergent gauge fields, the Quantum Hall Effect (integer and fractional), anyonic statistics34. Chern–Simons and self-duality in odd dimensions, its duality to topologically massive theory and dualities in general35. Particle-vortex duality in 3 dimensions, particle-string duality in 4 dimensions, and p-form fields in 4 dimensions36. Fermions and Dirac spinors37. The Dirac equation at its solutions38. General relativitymetric and general coordinate invariance39. The Einstein action and the Einstein equation40. Perturbative gravityFierz–Pauli action, de Donder gauge and other gauges, gravitational waves41. Nonperturbative gravitythe vacuum Schwarzschild solution42. Deflection of light by the Sun and comparison with general relativity43. Fully linear gravityparallel plane (pp) waves and gravitational shockwave solutions44. Dimensional reductionthe domain wall, cosmic string and BTZ black hole solutions45. Time dependent gravitythe Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological solution46. Vielbein-spin connection formulation of general relativity and gravitational instantonsReferencesIndex.
