The QCD string with quarks in external electromagnetic fields

Using the QCD string theory developed previously by Simonov we have introduced the interaction with constant external electromagnetic fields. The effective action was obtained in the non-relativistic case. We calculated the charge radius of pions 〈rπ±〉 = 0.84 fr and their electric polarizability απ± = 0.22 × 10−4fm3 which are in agreement with the experiment.