We consider the large order behavior of the perturbative expansion of the scalar φ4field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additional Feynman diagram with respect to the previously known one dimensional case, but a careful treatment of renormalization is needed. The propagator and Feynman diagrams were expressed in a form suitable for numerical evaluation. We then obtained explicit expressions summing over O(10^3) distinct eigenvalues determined numerically with the corresponding eigenfunctions.
Two-loop corrections to large order behavior of phi(4) theory / E.M. Malatesta, G. Parisi, T. Rizzo. - In: NUCLEAR PHYSICS. B. - ISSN 0550-3213. - 922(2017 Sep), pp. 293-318.
Two-loop corrections to large order behavior of phi(4) theory
E.M. Malatesta;
2017
Abstract
We consider the large order behavior of the perturbative expansion of the scalar φ4field theory in terms of a perturbative expansion around an instanton solution. We have computed the series of the free energy up to two-loop order in two and three dimension. Topologically there is only an additional Feynman diagram with respect to the previously known one dimensional case, but a careful treatment of renormalization is needed. The propagator and Feynman diagrams were expressed in a form suitable for numerical evaluation. We then obtained explicit expressions summing over O(10^3) distinct eigenvalues determined numerically with the corresponding eigenfunctions.File | Dimensione | Formato | |
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