Abstract:
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.