https://doi.org/10.1140/epjc/s10052-019-6739-y
Regular Article - Theoretical Physics
Background field method in the large 
expansion of scalar QED
1
Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China
2
School of Physical Sciences, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, 100049, China
3
Center for Astrophysics, Guangzhou University, Guangzhou, 510006, People’s Republic of China
4
Guangzhou University Library, Guangzhou University, Guangzhou, 510006, People’s Republic of China
* e-mail: zhengzy@itp.ac.cn
Received:
25
September
2018
Accepted:
1
March
2019
Published online:
11
March
2019
Using the background field method, we, in the large approximation, calculate the beta function of scalar quantum electrodynamics at the first nontrivial order in 
by two different ways. In the first way, we get the result by summing all the graphs contributing directly. In the second way, we begin with the Borel transform of the related two point Green’s function. The main results are that the beta function is fully determined by a simple function and can be expressed as an analytic expression with a finite radius of convergence, and the scheme-dependent renormalized Borel transform of the two point Green’s function suffers from renormalons.
© The Author(s), 2019
