Quantization of bosonic string field and infinite-dimensional pseudodifferential operators. Fixed gauge

Gaussian measure is introduced which is associated with the Bosonic string field in the light cone gauge. String quantization and quantization of Bosonic string field is performed in the framework of the theory of pseudodifferential operators on the space with the fixed Gaussian measure. Another approach to quantization, the quantization in the Schrödinger representation, is also considered. The Hilbert space structure cannot be introduced in the space in which the Schrödinger representation for infinitedimensional systems is realized. Problem of quantization in non-Hilbertian spaces is discussed. Hamiltonian of Bosonic string field with polynomial self-interaction is constructed.