Interacting Scalar Fields

  • Mikko Laine
  • Aleksi Vuorinen
Part of the Lecture Notes in Physics book series (LNP, volume 925)


The key concepts of a perturbative or weak-coupling expansion are introduced in the context of evaluating the imaginary-time path integral representation for the partition function of an interacting scalar field. The issues of ultraviolet and infrared divergences are brought up. These problems are cured through renormalization and resummation, respectively.


Contraction Propagator Renormalization Resummation Ring diagrams Ultraviolet and infrared divergences Weak-coupling expansion Wick’s theorem 


  1. 1.
    A. Gynther, M. Laine, Y. Schröder, C. Torrero, A. Vuorinen, Four-loop pressure of massless O(N) scalar field theory. J. High Energy Phys. 04, 094 (2007) [hep-ph/0703307].Google Scholar
  2. 2.
    J.O. Andersen, L. Kyllingstad, L.E. Leganger, Pressure to order \(g^{8}\log g\) of massless ϕ 4 theory at weak coupling. J. High Energy Phys. 08, 066 (2009) [0903.4596]Google Scholar
  3. 3.
    P.B. Arnold, O. Espinosa, The Effective potential and first order phase transitions: beyond leading order. Phys. Rev. D 47, 3546 (1993); ibid. D 50, 6662 (E) (1994) [hep-ph/9212235]Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mikko Laine
    • 1
  • Aleksi Vuorinen
    • 2
  1. 1.AEC, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.Department of PhysicsUniversity of HelsinkiHelsinkiFinland

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