lightcone gauge). Consequently, the problem can be set up directly for the Nambu – Goto String rather than the Polyakov – String. Therefore, Conformal Field Theory Methods never play even the slightest role because there is never any need to introduce and eventually fix any worldsheet metric. Notice also that by definition we only consider representations without Virasoro and Lorentz anomalies, the central charge is zero by definition. Finally, in the modern framework of QFT [@3] there is no need for mathematically ill – defined objects such as negative norm states (ghosts) in the Gupta – Bleuler quantization procedure so that all our representations will be ghost – free by definition.

The above mentioned three frameworks can now be combined as follows: The [**Pohlmeyer Charges**]{} provide the algebra to be quantized, [**AQFT**]{} provides us with techniques to construct representations and finally [**LQG**]{} equips us with methods to obtain representations of the algebra of invariants from diffeomorphism invariant representations of kinematical (not gauge invariant) observables.

In this paper we set up the general framework for the representation theory of the closed bosonic string on flat target space and present a non – trivial solution thereof. This solution exists in any target 