The European Physical Journal C

, Volume 56, Issue 4, pp 585–590 | Cite as

A renormalized perturbation theory for problems with non-trivial boundary conditions or backgrounds in two space–time dimensions

  • Reza Moazzemi
  • Abdollah Mohammadi
  • Siamak S. GoushehEmail author
Regular Article - Theoretical Physics


We discuss the effects of non-trivial boundary conditions or backgrounds, including non-perturbative ones, on the renormalization program for systems in two dimensions. We present an alternative renormalization procedure in which these non-perturbative conditions can be taken into account in a self-contained and, we believe, self-consistent manner. These conditions have profound effects on the properties of the system, in particular all of its n-point functions. To be concrete, we investigate these effects in the λ φ 4 model in two dimensions and show that the mass counterterms turn out to be proportional to the Green’s functions which have a non-trivial position dependence in these cases. We then compute the difference between the mass counterterms in the presence and absence of these conditions. We find that in the case of non-trivial boundary conditions this difference is minimum between the boundaries and infinite on them. The minimum approaches zero when the boundaries go to infinity. In the case of non-trivial backgrounds, we consider the kink background and show that the difference is again small and localized around the kink.


Soliton Solitary Wave Zero Mode Casimir Energy Renormalization Procedure 
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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  • Reza Moazzemi
    • 1
  • Abdollah Mohammadi
    • 1
  • Siamak S. Gousheh
    • 1
    Email author
  1. 1.Department of PhysicsShahid Beheshti University G. C.TehranIran

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