Possibility of constructing a gauge-invariant quantum formulation for nongauge classical theory

A general method is proposed for the construction of a gauge-invariant canonical quantum formulation for the gauge-invariant classical theory that depends on the set of parameters. The conditions for closure of the algebra of operators, which generate quantum gauge transformations, entails constraints on the parameters of the theory. The approach described is demonstrated by the example of a closed bosonic string, interacting with a background tachyonic field. The condition of a mass shell for the tachyon is reproduced within the framework of the proposed canonical formulation. Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 18–24, June, 1997.