 
Summary: NOTE BREVI
IL NUOVO CIMENTO VOL. 111 A, N. 3 Marzo 1998
Power counting degree vs. singular order
in the Schwinger model
A. ASTE, G. SCHARF and U. WALTHER
Institut f¨ur Theoretische Physik der Universit¨at Z¨urich,
Winterthurerstr. 190, CH8057 Z¨urich, Switzerland
(ricevuto l'8 Maggio 1998; approvato il 26 Maggio 1998)
Summary.  The importance of a rigorous definition of the singular degree of a distri
bution is demonstrated in the case of twodimensional QED (Schwinger model). Cor
rect mathematical treatment of secondorder vacuum polarization in the perturbative
approach is crucial in order to obtain the Schwinger mass of the photon by resumma
tion.
PACS 11.10 Field theory.
PACS 11.15 Gauge field theory.
1. Introduction
The Schwinger model [1] still serves as a very popular laboratory for quantum field
theoretical methods. Although its nonperturbative properties and their relations to con
finement [2,3] have always been of greatest interest, it is also possible to discuss the model
perturbatively in a straightforward way. The calculation of the vacuum polarization dia
