The distributional Borel summability and the large coupling \(\Phi ^ 4\) lattice fields. (English) Zbl 0648.40007

Following ’t Hooft we extend the Borel sum and the Watson-Nevanlinna criterion by allowing distributional transforms. This enables us to prove that the characteristic function of the measure of any \(g^{-2}\Phi^ 4\) finite lattice field is the sum of a power series expansion obtained by fixing exponentially small terms in the coefficients. The same result is obtained for the trace of the double well semigroup approximated by the n th order Trotter formula.


40G10 Abel, Borel and power series methods
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