Quantum string theory in the space of states in an indefinite metric

The quantum string theory in the indefinite (pseudo-Hilbert) Fock representation is considered. It is shown that all anomalies in the four-dimensional theory of an open bosonic string are canceled for a particular choice of the vacuum state. Then the algebra of the reparametrization symmetry (in the covariant approach) and the algebra of rotations (in the light-cone gauge) become closed. The indefiniteness of the space of states leads to some nonphysical properties of the theory. Modifications of the model under consideration, which are necessary to construct a more realistic theory, are discussed.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 213–228, May, 1996.Translated by L. O. Chekhov.