Abstract
In a preceding article a Matthews-Salam formula was constructed for the Schwinger functions (vacuum expectation values of polynomials in the fields) of Euclidean QED 2 on a periodic lattice. For any combination of gauge or fermion fields S on a lattice with spacing proportional to N −1, N ϵ Z +, the Matthews-Salam formula for the vacuum expectation 〈 S〉 N has the form 〈 G〉 N =∫ dμW N ( G. f),, where μ is an N-independent measure on a random electromagnetic field f and W N ( S, f) in an N-dependent function of f and S . In the present article we prove that the limit of ∫ dμW N ( G. f) exists as N → ∞ and has the form lim N→∞ ∫ dμW N ( G. f)=∫ dμW( G. f), where W( S, f) is in L p ( μ) for all p, ∞ > p > 0.
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