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
Most perturbation expansions in quantum mechanics are divergent for any small coupling strength
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. Applications focus on the theory of critical phenomena. It has led to the most accurate predictions of critical exponents. More details can be read here.