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arXiv · 0806.2679

Quantum corrections to static solutions of Nahm equation and Sin-Gordon models via generalized zeta-function

Sergey Leble
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Abstract

One-dimensional Yang-Mills Equations are considered from a point of view of a class of nonlinear Klein-Gordon-Fock models. The case of self-dual Nahm equations and non-self-dual models are discussed. A quasiclassical quantization of the models is performed by means of generalized zeta-function and its representation in terms of a Green function diagonal for a heat equation with the correspondent potential. It is used to evaluate the functional integral and quantum corrections to mass in the quasiclassical approximation. Quantum corrections to a few periodic (and kink) solutions of the Nahm as a particular case of the Ginzburg-Landau (phi-in-quadro) and and Sin-Gordon models are evaluated in arbitrary dimensions. The Green function diagonal for heat equation with a finite-gap potential is constructed by universal description via solutions of Hermit equation. An alternative approach based on Baker-Akhiezer functions for KP equation is proposed . The generalized zeta-function and its derivative at zero point as the quantum corrections to mass is expressed in terms of elliptic integrals.

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Sergey Leble. 2009-01-12. Quantum corrections to static solutions of Nahm equation and Sin-Gordon models via generalized zeta-function. https://doi.org/10.1007/s11232-009-0088-1

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