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 $\text{G}$ on a lattice with spacing proportional to N^?1, N?Z⁺, the Matthews-Salam formula for the vacuum expectation 〈G〉_N has the form ($\text{G}$)_N=∫d_nu;W_N($\text{G}$,f), where dμ is an N-independent measure on a random electromagnetic field ? and $\text{W}{}_{\mathrm{N}}\text{(G, ?)}$ is an N-dependent function of ? determined by $\text{G}$. For a class of $\text{G}$ we prove that as N → ∞, $\text{W}{}_{\mathrm{N}}\text{(C, ?)}$ has a limit $\text{W(G, ?)}$ except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫d_nu;W_N($\text{G}$,f) exists and lim_N→∞∫d_nu;W_N($\text{G}$,f).