In mathematics, variational perturbation theory (VPT) is a mathematical method to convert divergent power series in a small expansion parameter, say into a convergent series in powers where
is a critical exponent (the so-called index of "approach to scaling" introduced by Franz Wegner).
[1] Most perturbation expansions in quantum mechanics are divergent for any small coupling strength
They can be made convergent by VPT (for details see the first textbook cited below).
[2][3] After its success in quantum mechanics, VPT has been developed further to become an important mathematical tool in quantum field theory with its anomalous dimensions.