Regular Article - Theoretical Physics
Logarithmic expansion of field theories: higher orders and resummations
Department of Physics and Astronomy, University of Catania, Via Santa Sofia 64, 95123, Catania, Italy
2 INFN, Sezione di Catania, Via Santa Sofia 64, 95123, Catania, Italy
3 Scuola Superiore di Catania, Via Valdisavoia 9, 95123, Catania, Italy
Accepted: 27 May 2021
Published online: 22 June 2021
A formal expansion for the Green’s functions of a quantum field theory in a parameter that encodes the “distance” between the interacting and the corresponding free theory was introduced in the late 1980s (and recently reconsidered in connection with non-hermitian theories), and the first order in was calculated. In this paper we study the systematically, and also push the analysis to higher orders. We find that at each finite order in the theory is non-interacting: sensible physical results are obtained only resorting to resummations. We then perform the resummation of UV leading and subleading diagrams, getting the and weak-coupling results. In this manner we establish a bridge between the two expansions, provide a powerful and unique test of the logarithmic expansion, and pave the way for further studies.
© The Author(s) 2021
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