Classical Field Theory

Horaƫiu Năstase

doi:10.1017/9781108569392

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Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo

Publisher:: Cambridge University Press
Online publication date:: March 2019
Print publication year:: 2019
Online ISBN:: 9781108569392
DOI:: https://doi.org/10.1017/9781108569392

Subjects:: Physics and Astronomy, Theoretical Physics and Mathematical Physics, General and Classical Physics

67.00 (GBP)

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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.

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Classical Field Theory

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Contents

23 - Radiation of a Classical Scalar Field: The Heisenberg Model
pp 209-216

24 - Derrick’s Theorem, Bogomolnyi Bound, theAbelian-Higgs System, andSymmetryBreaking
pp 217-225

25 - The Nielsen-Olesen Vortex, Topology and Applications
pp 226-235

26 - Non-Abelian Gauge Theory and the Yang–Mills Equation
pp 236-243

27 - The Dirac Monopole and Dirac Quantization
pp 244-255

28 - The ’t Hooft–Polyakov Monopole Solution and Topology
pp 256-266

29 - The BPST-’t Hooft Instanton Solution and Topology
pp 267-277

30 - General Topology and Reduction on an Ansatz
pp 278-284

31 - Other Soliton Types. Nontopological Solitons: Q-Balls; Unstable Solitons: Sphalerons
pp 285-293

32 - Moduli Space; Soliton Scattering in Moduli Space Approximation; Collective Coordinates
pp 294-306

Part III - Other Spins or Statistics; General Relativity
pp 307-308

33 - Chern–Simons Terms: Emergent Gauge Fields, the Quantum Hall Effect (Integer and Fractional), Anyonic statistics
pp 309-318

34 - Chern–Simons and Self-Duality in Odd Dimensions, Its Duality to Topologically Massive Theory and Dualities in General
pp 319-329

35 - Particle–Vortex Duality in Three Dimensions, Particle–String Duality in Four Dimensions, and p-Form Fields in Four Dimensions
pp 330-337

36 - Fermions and Dirac Spinors
pp 338-346

37 - The Dirac Equation and Its Solutions
pp 347-355

38 - General Relativity: Metric and General Coordinate Invariance
pp 356-366

39 - The Einstein Action and the Einstein Equation
pp 367-377

40 - Perturbative Gravity: Fierz-Pauli Action, de Donder Gauge and Other Gauges, Gravitational Waves
pp 378-388

41 - Nonperturbative Gravity: The Vacuum Schwarzschild Solution
pp 389-395

42 - Deflection of Light by the Sun and Comparison with General Relativity
pp 396-404

43 - Fully Linear Gravity: Parallel Plane (pp) Waves and Gravitational Shock Wave Solutions
pp 405-417

44 - Dimensional Reduction: The Domain Wall, Cosmic String, and BTZ Black Hole Solutions
pp 418-432

45 - Time-Dependent Gravity: The Friedmann-Lemaître-Robertson-Walker (FLRW) Cosmological Solution
pp 433-440

46 - Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
pp 441-454

References
pp 455-457

Index
pp 458-462

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