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Classical Field Theory

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  • Date Published: March 2019
  • availability: In stock
  • format: Hardback
  • isbn: 9781108477017

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  • Classical 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.

    • Focuses on classical field theory aspects for electromagnetism and general relativity, allowing readers to focus on methods rather than physical applications
    • Provides a bridge between classical mechanics and quantum field theory, helping the reader navigate the conceptual gap
    • Includes up-to-date and comprehensive coverage of modern methods of classical field theory
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    Product details

    • Date Published: March 2019
    • format: Hardback
    • isbn: 9781108477017
    • length: 480 pages
    • dimensions: 253 x 192 x 26 mm
    • weight: 1.2kg
    • contains: 37 b/w illus.
    • availability: In stock
  • Table of Contents

    Preface
    Introduction
    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
    water waves, 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 electromagnetic waves
    Maxwell duality
    16. The Hopfion solution and the Hopf map
    17. Complex scalar field and electric current. Gauging a global symmetry
    18. The Noether theorem and applications
    19. Nonrelativistic and relativistic fluid dynamics. Fluid vortices and knots
    20. Kink solutions in ø4 and sine-Gordon, domain walls and topology
    21. The Skyrmion scalar field solution and topology
    22. Field theory solitons for condensed matter: the XY and rotor model, spins, superconductivity and the KT transition
    23. Radiation of a classical scalar field. The Heisenberg model
    24. Derrick's theorem, Bogomolnyi bound, the Abelian–Higgs system and symmetry breaking
    25. The Nielsen–Olesen vortex, topology and applications
    26. Nonabelian gauge theory and the Yang–Mills equation
    27. The Dirac monopole and Dirac quantization
    28. The 't Hooft–Polyakov monopole solution and topology
    29. The BPST-'t Hooft instanton solution and topology
    30. General topology and reduction on an ansatz
    31. Other soliton types. Nontopological solitons: Q-balls
    unstable solitons: sphalerons
    32. Moduli space
    soliton scattering in moduli space approximation
    collective coordinates
    33. Chern–Simons terms: emergent gauge fields, the Quantum Hall Effect (integer and fractional), anyonic statistics
    34. Chern–Simons and self-duality in odd dimensions, its duality to topologically massive theory and dualities in general
    35. Particle-vortex duality in 3 dimensions, particle-string duality in 4 dimensions, and p-form fields in 4 dimensions
    36. Fermions and Dirac spinors
    37. The Dirac equation at its solutions
    38. General relativity: metric and general coordinate invariance
    39. The Einstein action and the Einstein equation
    40. Perturbative gravity: Fierz–Pauli action, de Donder gauge and other gauges, gravitational waves
    41. Nonperturbative gravity: the vacuum Schwarzschild solution
    42. Deflection of light by the Sun and comparison with general relativity
    43. Fully linear gravity: parallel plane (pp) waves and gravitational shockwave solutions
    44. Dimensional reduction: the domain wall, cosmic string and BTZ black hole solutions
    45. Time dependent gravity: the Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological solution
    46. Vielbein-spin connection formulation of general relativity and gravitational instantons
    References
    Index.

  • Author

    Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
    Horaƫiu Năstase is a Researcher at the Institute for Theoretical Physics at the Universidade Estadual Paulista, São Paulo. To date, his career has spanned four continents. As an undergraduate he studied at the Universitatea din București and Københavns Universitet. He later completed his Ph.D. at the State University of New York, Stony Brook, before moving to the Institute for Advanced Study, Princeton University, New Jersey, where his collaboration with David Berenstein and Juan Maldacena defined the pp-wave correspondence. He has also held research and teaching positions at Brown University, Rhode Island and the Tokyo Institute of Technology.

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