Speaker
Description
Gell-Mann-Low functions in quantum field theory are usually defined as asymptotic expansions over a small coupling. However their behavior at large coupling is of principal interest, since this behavior sheds light on the general properties of the coupling parameter as a function of a scale variable. We developed an approach, called self-similar approximation theory, allowing for the extrapolation of asymptotic
expansions over a small variable to finite and even infinite values of the variable. The approach is illustrated by several examples demonstrating the convergence of the found strong-coupling exponent to exactly known values. Then the self-similar extrapolation is applied for finding out strong-coupling exponents of perturbative expansions over asymptotically weak coupling for the Gell-Mann-Low functions of
multicomponent scalar field theory, quantum electrodynamics, and quantum chromodynamics.
