Relativistic string in a constant homogeneous electromagnetic field

The Lagrangian and Hamiltonian formalisms are constructed for the massless relativistic string in constant homogeneous electromagnetic field in a special gauge dependent on the field. Solutions to the equations of motion and the mass spectrum of the string are found. It is shown that the presence of the electric field increases the gap between the equidistant levels of the squared mass operator, as compared with the free string case. The quantum description of the string in electromagnetic field is considered and the problem of the relativistic invariance of quantum theory is discussed. The method based on the checking of the Poincare algebra turns out to be inapplicable in the presence of the external field, because in this case the Lorentz rotation operators become time-dependent.