ar X iv : h ep - t h / 94 03 14 8 v 2 2 8 M ar 1 99 4 INFINITE DIMENSIONAL GEOMETRY AND QUANTUM FIELD THEORY OF STRINGS

A geometric interpretation of quantum self–interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorythm to construct a quantum nonperturbative interacting string field theory in the quantum group formalism is proposed. Problems of a metric background (in)dependence are discussed. This is the second part of the paper devoted to various structures of an infinite dimensional geometry, appearing in quantum field theory of (closed) strings; the objects connected with the second quantization of a free string were described in the first part [1], whereas an analogous material for a self–interacting string field will be discussed now. It is proposed to continue the investigation of an infinite dimensional geometry related to the quantum field theory of strings in the following two parts (parts III,IV). The third part is devoted to an infinite dimensional W –geometry of a second quantized free string [2]; the fourth part should contain materials on infinite dimensional geometry of a self–interacting W –string field. In the whole paper we follow a general ideology of string theory presented in [3]. All four parts of the publication maybe considered as a sequel of previous one [4] devoted to geometric aspects of quantum conformal field theory: the transition from the 2D quantum conformal field theory to the self–interacting string field theory maybe considered as one from the abstract geometry of noncommutative Riemann