Variational perturbation theory
In mathematics, variational perturbation theory 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. This is possible with the help of variational parameters, which are determined by optimization order by order in. The partial sums are converted to convergent partial sums by a method developed in 1992.
Most perturbation expansions in quantum mechanics are divergent for any small coupling strength. They can be made convergent by VPT. The convergence is exponentially fast.
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.
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