In:
Journal of High Energy Physics, Springer Science and Business Media LLC, Vol. 2019, No. 3 ( 2019-03)
Abstract:
We study the three-loop Euler-Heisenberg Lagrangian in spinor quantum electrodynamics in 1+1 dimensions. In this first part we calculate the one-fermion-loop contribution, applying both standard Feynman diagrams and the worldline formalism which leads to two different representations in terms of fourfold Schwinger-parameter integrals. Unlike the diagram calculation, the worldline approach allows one to combine the planar and the non-planar contributions to the Lagrangian. Our main interest is in the asymptotic behaviour of the weak-field expansion coefficients of this Lagrangian, for which a non-perturbative prediction has been obtained in previous work using worldline instantons and Borel analysis. We develop algorithms for the calculation of the weak-field expansion coefficients that, in principle, allow their calculation to arbitrary order. Here for the non-planar contribution we make essential use of the polynomial invariants of the dihedral group D 4 in Schwinger parameter space to keep the expressions manageable. As expected on general grounds, the coefficients are of the form r 1 + r 2 ζ 3 with rational numbers r 1 , r 2 . We compute the first two coefficients analytically, and four more by numerical integration.
Type of Medium:
Online Resource
ISSN:
1029-8479
DOI:
10.1007/JHEP03(2019)167
Language:
English
Publisher:
Springer Science and Business Media LLC
Publication Date:
2019
detail.hit.zdb_id:
2027350-2
Permalink