Three-loop Correction to the Instanton Density. I. The Quartic Double Well Potential
Abstract
This paper deals with quantum fluctuations near the classical instanton configuration. Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude (the instanton density) in the three-loop order for quartic double-well potential. The result for the three-loop contribution coincides in six significant figures with one given long ago by J.~Zinn-Justin. Unlike the two-loop contribution where all involved Feynman integrals are rational numbers, in the three-loop case Feynman diagrams can contain irrational contributions.
Cite
@article{arxiv.1501.03993,
title = {Three-loop Correction to the Instanton Density. I. The Quartic Double Well Potential},
author = {M. A. Escobar-Ruiz and E. Shuryak and A. V. Turbiner},
journal= {arXiv preprint arXiv:1501.03993},
year = {2015}
}
Comments
15 pages, 3 figures, 1 table, already published at Phys.Rev.D92 (2015) 025046, 089902(erratum), a post published version with tadpole diagrams redrawn to clearly mark the Jacobian source and misprint on 3-loop tadpole contribution on p.8 fixed