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23 February 2020
  » arxiv » hep-th/9801054

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Exact solution for a quantum field with $delta$-like interaction
Sergey N. Solodukhin ;
Date 9 Dec 1997
Journal Nucl.Phys. B541 (1999) 461-482
Subject High Energy Physics - Theory; Exactly Solvable and Integrable Systems | hep-th gr-qc nlin.SI solv-int
AbstractA quantum field described by the field operator $Delta_{a}=Delta+ adelta_Sigma$ involving a $delta$-like potential is considered. Mathematically, the treatment of the $delta$-potential is based on the theory of self-adjoint extension of the unperturbed operator $Delta$. We give the general expressions for the resolvent and the heat kernel of the perturbed operator $Delta_{a}$. The main attention is payed to $d=2$ $delta$-potential though $d=1$ and $d=3$ cases are considered in some detail. We calculate exactly the heat kernel, Green’s functions and the effective action for the operator $Delta_{a}$ in diverse dimensions and for various spaces $Sigma$. The renormalization phenomenon for the coupling constant $a$ of $d=2$ and $d=3$ $delta$-potentials is observed. We find the non-perturbative behavior of the effective action with respect to the renormalized coupling $a_{ren}$.
Source arXiv, hep-th/9801054
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