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On Field Theory Methods in Singular Perturbation Theory |
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| Authors: | Kurasov P. Pavlov Yu. V. |
| Affiliation: | (1) Department of Mathematics, Lund Institute of Technology, Box 118, 22100 Lund, Sweden;(2) Institute for Physics, St. Petersburg University, 198904 St. Petersburg, Russia;(3) A. Friedmann Laboratory for Theoretical Physics, 30/32 Griboedov can., St. Petersburg, 191023, Russia;(4) Institute of Mechanical Engineering, Russian Academy of Sciences, 61 Bolshoy, V.O., St. Petersburg, 199178, Russia |
| 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. |
| Keywords: | quantum field theory renormalization self-adjoint operator singular perturbation |
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