  We describe a covariant framework to construct a globalized version for the
perturbative quantization of nonlinear split AKSZ Sigma Models on manifolds
with and without boundary, and show that it captures the change of the quantum
state as one changes the constant map around which one perturbs. This is done
by using concepts of formal geometry. Moreover, we show that the globalized
quantum state can be interpreted as a closed section with respect to an
operator that squares to zero. This condition is a generalization of the
modified Quantum Master Equation as in the BV-BFV formalism, which we call the
modified "differential" Quantum Master Equation.
