Letters in Mathematical Physics

, Volume 64, Issue 2, pp 171–184 | Cite as

On Field Theory Methods in Singular Perturbation Theory

  • P. Kurasov
  • Yu. V. Pavlov
Article

Abstract

Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli–Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms.

quantum field theory renormalization self-adjoint operator singular perturbation 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • P. Kurasov
    • 1
    • 2
  • Yu. V. Pavlov
    • 3
    • 4
  1. 1.Department of MathematicsLund Institute of TechnologyLundSweden
  2. 2.Institute for PhysicsSt. Petersburg UniversitySt. PetersburgRussia
  3. 3.A. Friedmann Laboratory for Theoretical PhysicsSt. PetersburgRussia
  4. 4.Institute of Mechanical EngineeringRussian Academy of SciencesSt. PetersburgRussia

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