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Exact solution for a quantum field with $delta$-like interaction | | Sergey N. Solodukhin
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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 | | Abstract: | A 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 | | Services: | Forum | Review | PDF | Favorites | |
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