smeared the constraints with smooth test functions of rapid decrease, that is, $C(N)=\int_\sigma d^{p-1}x N C$ and $D(\vec{N})=\int_M d^{p-1}x N^a D_a$.

Notice that precisely when $p=2$ we have that $\det(q) q^{ab}=1$ is a constant. Thus, among all $p-$brane actions the string is singled out by the fact that its constraints form an honest Lie Poisson algebra. For $p>2$ we get nontrivial structure functions just like for General Relativity. We will strongly exploit this fact for the rest of the paper for which we restrict our attention to the case $p=2$ and $\eta$ is the target space Minkowski metric $\eta=$diag$(-1,1,..,1)$. See our companion paper [@11] for the more general case.

Notice that throughout our analysis we have not introduced a worldsheet metric and there is no Weyl symmetry at all. The only local worldsheet symmetry is Diff$(M)$. Also we work manifestly gauge free, that is, we never (partially) fix Diff$(M)$, there is no conformal gauge or anything like that. Finally we want to construct a true Dirac quantization of the system, hence we do not introduce any gauge such as the lightcone gauge in order to solve the constraints classically. This will have the advantage to preserve manifest Lorentz invariance in 