We consider the large order behavior of the perturbative expansion of the scalar φ4 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 φ4 theory

Enrico M. , Malatesta;
2017

Abstract

We consider the large order behavior of the perturbative expansion of the scalar φ4 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.
2017
2017
Malatesta, ENRICO MARIA; Parisi, Giorgio; Rizzo, Tommaso
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11565/4029516
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