Regge trajectories of the charged string in a magnetic background

The set of Casimir operators associated with the global symmetries of a charged string in a constant magnetic background are found. It is shown that the string rest energy can be expressed as a combination of these invariants. Using this result, the Regge trajectories of the system are derived. The first Regge trajectory is given by a family of infinitely many parallel straight-lines, one for each spin projection along the magnetic field.