https://doi.org/10.1140/epjc/s10052-021-09293-4
Regular Article - Theoretical Physics
Logarithmic expansion of field theories: higher orders and resummations
1
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
Received:
15
February
2021
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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
