We discuss a recently developed method of large charge expansion, which allows for obtaining new precise results in quantum field models with global symmetries. In this approach, anomalous dimensions of composite operators with fixed charge Q are considered. In the limit of large charge, they are found in the leading and subleading order in Q, but arbitrary order in interaction constants.

Until recently, the application of this method was limited to theories with global symmetries. We demonstrate how large-charge expansion can be used to obtain gauge-invariant predictions in scalar electrodynamics. An important check of the quasi-classical result is that in the limit of small coupling constants, the computed anomalous dimensions coincide with our direct three-loop calculations performed in the Landau gauge. The latter fact is interpreted as a nontrivial argument in favor of a certain choice of order parameter for type II superconductors.