Canonical approach to string theory in massive background fields

A method of constructing a canonical gauge-invariant quantum formulation for a non-gauge classical theory depending on a set of parameters is advanced and then applied to the theory of a closed bosonic string interacting with massive background fields. Choosing an ordering prescription and developing a suitable regularization technique, we calculate quantum gauge algebra up to linear order in background fields. The requirement of closure for the algebra leads to equations of motion for the massive background fields, which appear to be consistent with the structure of the string spectrum.