all steps of our construction.

[**Pohlmeyer Charges**]{} {#s3}
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In the rest of the paper we focus on the closed bosonic string, i.e. $p=2$ and $\sigma=S^1$ on flat Minkowski space. We take our spatial coordinate $x$ to be in the range $[0,2\pi)$. All functions in what follows are periodic with period $2\pi$ unless specified otherwise.\
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From the classical point of view we must find the (strong) Dirac observables of the system, that is, functions on the phase space coordinatized by $X,\pi$ which have (strongly) vanishing Poisson brackets with the constraints. While the string is a parameterized system so that the Hamiltonian defined by the Legendre transform vanishes identically, the initial value constraints do generate arbitrary time reparameterizations and in this sense the problem of finding the Dirac observables is closely related to finding the integrals of motion of a dynamical system [@14]. This leads us to the theory of integrable systems [@14a] and the very powerful techniques that have been developed for those, especially in two dimensions. Pohlmeyer et. al. have shown in an impressive series of papers [@6; @16; @7; @17] that the string is completely integrable. Since to the best of our knowledge these important works are 