We consider the large order behavior of the perturbative expansion of the scalar ?4 field 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(103) distinct eigenvalues determined numerically with the corresponding eigenfunctions
Two-loop corrections to large order behavior of phi4 theory
Parisi G.;Rizzo T.
2017
Abstract
We consider the large order behavior of the perturbative expansion of the scalar ?4 field 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(103) distinct eigenvalues determined numerically with the corresponding eigenfunctions| File | Dimensione | Formato | |
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Descrizione: Two-loop corrections to large order behavior of φ4 theory
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