Non-perturbative VEVs from a Local Expansion

TL;DR

The paper introduces a local expansion method to compute vacuum expectation values from complex vacuum wave functionals, using analytic continuation to handle divergences, demonstrated in 1+1 dimensional scalar theory.

Contribution

It presents a novel approach combining local expansion and analytic continuation to evaluate VEVs from non-trivial vacuum wave functionals.

Findings

Method successfully computes VEVs in 1+1D scalar theory.

Analytic continuation extends the applicability beyond the cutoff scale.

Framework applicable to theories like Yang-Mills with boundary divergences.

Abstract

We propose a method for the calculation of vacuum expectation values (VEVs) given a non-trivial, long-distance vacuum wave functional (VWF) of the kind that arises, for example, in variational calculations. The VEV is written in terms of a Schr\"odinger-picture path integral, then a local expansion for (the logarithm of the) VWF is used. The integral is regulated with an explicit momentum cut-off, $\Lambda$. The resulting series is not expected to converge for $\Lambda$ larger than the mass-gap but studying the domain of analyticity of the VEVs allows us to use analytic continuation to estimate the large-$\Lambda$ limit. Scalar theory in 1+1 dimensions is analyzed, where (as in the case of Yang-Mills) we do not expect boundary divergences.