Method of summing the perturbation series in scalar theories

A. G. Basuev ; A. N. Vasil'ev

Teoretičeskaâ i matematičeskaâ fizika, Tome 18 (1974) no. 2, pp. 181-189

Résumé

Taking as an example connected vacuum loops of the theory $-\lambda\varphi^4$, we consider a method of summing the perturbation series in which the number of graphs is allowed for exactly and the departure of the mean value of a graph from a purely power law is simulated by the substitution $\lambda\to\lambda e^{it}$ heit and subsequent averaging over $t$ with a weight $f(t)$ (the function $f$ remains unknown). The resulting expression is analytic in some sector, including the half-axis $\lambda>0$. At the point $\lambda=0$ there is an essential singularity generated by the concentric cuts that accumulate at the point $\lambda=0$ (the cuts are not included in the analyticity sector).