the string there is no Stone – von Neumann uniqueness theorem [@5] and the corresponding representation theory is usually very complex.

-   [III.]{} [*Integrable Systems (Pohlmeyer Charges)*]{}\
    In constrained dynamical systems it is highly non – trivial to identify the gauge invariant observables of the theory. It is even harder to find faithful representations of the corresponding, usually highly non – linear, commutation relations. Fortunately, for the closed bosonic string on flat target space the complete set of gauge invariant observables, the [**Pohlmeyer Charges**]{}, has been found [@6] and their classical Poisson algebra is under complete control [@16; @7; @17]. This will come to the surprise of most string theorists who are  used to work in the so – called conformal worldsheet and/or lightcone target space gauge. In contrast, these observables are manifestly gauge invariant and manifestly Lorentz covariant.

Hence, what we are looking for is a background independent, that is, gauge invariant (in the sense of [**LQG**]{}) and Lorentz invariant, representation (in the sense of [**AQFT**]{}) of the [**Pohlmeyer Algebra**]{}. Notice that by definition these representations do not allow us to pick either a worldsheet gauge (such as the conformal gauge) nor a target space gauge (such as the 