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2 results

  • 6 - Scalar Field Theory, Origins, and Applications

  • from Part I - General Properties of Fields; Scalars and Gauge Fields
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 54-64

  • Summary

    We define scalar field theory, explaining its various applications in physics as either fundamental or effective field. We write a general canonical Lagrangian with a potential, and the resulting Klein–Gordon equation.Examples for this are shown, in particular the sine–Gordon model and the Higgs model. For several scalars, we show the O(N) model and, for models with a noncanonical kinetic term, the DBI model and nonlinear sigma models.

  • 20 - Kink Solutions in ϕ4 and Sine-Gordon, Domain Walls and Topology

  • from Part II - Solitons and Topology; Non-Abelian Theory
  • Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
  • Book:
    Classical Field Theory
    Published online:
    04 March 2019
    Print publication:
    14 March 2019, pp 185-194

  • Summary

    We consider “kink” solutions of 1+1 dimensional scalar field models with a canonical kinetic term and a potential for the scalar. Classical, static, soliton solutions are found as solutions of the classical mechanics motion in an inverted (V = -U) potential. The cases of the $\phi^4$ and Higgs models are analyzed, and the Higgs “kink” solution is found and described. The sine–Gordon model is also analyzed and its soliton found. The topology of the solutions is characterized. Finally, embedding of the solution in higher dimensions as a “domain wall” is also considered.