Covariant formalism for a relativistic string in a constant homogeneous electromagnetic field

Covariant formalism for relativistic string in constant homogeneous electromagnetic field is developed. Solutions to the equations of motion are found in the form of the Fourier series. The subsidiary conditions which are expressed in terms of normal modes and are imposed on the state vectors are the same as in the free dual string theory. The operator of the squared mass of the string is obtained also. In the region where the solution obtained are applicable, $|gE/\gamma|<1$, the distance between the equidistant levels increases as compared with the free string case. The physical space of the state vectors with positive norm is constructed in the centre-of-mass frame. As a result, there are no restrictions on the space-time dimension, the quantum theory is relativistic invariant and has no tachyon states.