CONTINUUM LIMIT OF QED2 ON A LATTICE

A path integral is defined for the vacuum expectation values of Euclidean QED2 on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields G on a lattice with spacing proportional to N-1, N ε{lunate} Z+, the Matthews-Salam formula for the vacuum expectation 〈G〉N has the form (G)N=∫dnu;WN(G,f), where dμ is an N-independent measure on a random electromagnetic field f{hook} and WN(G, f{hook}) is an N-dependent function of f{hook} determined by G. For a class of G we prove that as N → ∞, WN(C, f{hook}) has a limit W(G, f{hook}) except possibly for a set of f{hook} of measure zero. In subsequent articles it will be shown that ∫dnu;WN(G,f) exists and limN→∞∫dnu;WN(G,f). © 1979.