we recall basics from Loop Quantum Gravity (LQG). In particular, we review the background independent canonical quantization programme which aims at constructing the physical Hilbert space, on which the quantum constraints are identically satisfied, from a given kinematical representation of an algebra of non – gauge invariant operators. The reason for not considering the algebra of invariants right away is that the complete set of invariants is rarely known explicitly for a sufficiently complicated theory (e.g. General Relativity). However, if the kinematical algebra separates the points of the full phase space then the invariant algebra is contained (possibly as a limit) in the kinematical algebra and hence the kinematical representation is a representation of the invariants as well, generically with quantum corrections. The kinematical representation is admissable, however, only if the physical representation induced from it still carries a representation of the invariants. It is in this step that non – trivial regularization techniques come into play.

In section six we collect the results of sections three, four and five to formulate the general representation problem of the closed bosonic string on flat target space. We then present a non – trivial solution to it. Basically, we found a worldsheet 