Three-loop Correction to the Instanton Density. II. The Sine-Gordon potential
Abstract
In this second paper on quantum fluctuations near the classical instanton configurations, see {\em Phys. Rev. D \bf 92}, 025046 (2015) and arXiv:1501.03993, we focus on another well studied quantum-mechanical problem, the one-dimensional Sine-Gordon potential (the Mathieu potential). Using only the tools from quantum field theory, the Feynman diagrams in the instanton background, we calculate the tunneling amplitude (the instanton density) to the three-loop order. The result confirms (to seven significant figures) the one recently recalculated by G. V. Dunne and M. \"{U}nsal, {\it Phys. Rev. \bf D 89}, 105009 (2014) from the resurgence perspective. As in the double well potential case, we found that the largest contribution is given by the diagrams originating from the Jacobian. We again observe that in the three-loop case individual Feynman diagrams contain irrational contributions, while their sum does not.
Cite
@article{arxiv.1505.05115,
title = {Three-loop Correction to the Instanton Density. II. The Sine-Gordon potential},
author = {M. A. Escobar-Ruiz and E. Shuryak and A. V. Turbiner},
journal= {arXiv preprint arXiv:1505.05115},
year = {2015}
}
Comments
14 pages, 3 figures, 1 table, already published at Phys.Rev.D: a post published version with tadpole diagrams redrawn to mark clearly the Jacobian source, Note Added about significance of a tadpole diagram in 3-,4-,5-loops contributions