Kurasov, P.; Pavlov, Yu. V. On field theory methods in singular perturbation theory. (English) Zbl 1038.81025 Lett. Math. Phys. 64, No. 2, 171-184 (2003). Summary: 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 regularizations can be applied to determine uniquely certain finite rank supersingular perturbations. The approach is based on the regularization of homogeneous singular quadratic forms. Cited in 3 Documents MSC: 81Q15 Perturbation theories for operators and differential equations in quantum theory 81T16 Nonperturbative methods of renormalization applied to problems in quantum field theory 47B25 Linear symmetric and selfadjoint operators (unbounded) 47N50 Applications of operator theory in the physical sciences 81T17 Renormalization group methods applied to problems in quantum field theory Keywords:quantum field theory; renormalization; self-adjoint operator; singular perturbation PDFBibTeX XMLCite \textit{P. Kurasov} and \textit{Yu. V. Pavlov}, Lett. Math. Phys. 64, No. 2, 171--184 (2003; Zbl 1038.81025) Full Text: DOI