  The zigzag model is a relativistic integrable $N$-body system describing the
leading high-energy semiclassical dynamics on the worldsheet of long confining
strings in massive adjoint two-dimensional QCD. We discuss quantization of this
model. We demonstrate that to achieve a consistent quantization of the model it
is necessary to account for the non-trivial geometry of phase space. The
resulting Poincar\'e invariant integrable quantum theory is a close cousin of
$T\bar{T}$ deformed models.
