adding some technical conditions.

The freedom which is left by the conditions [**LCSE-1...4**]{} for the quantized stress energy tensor of a local covariant quantum field theory can be traced back to the circumstance that even in such a simple theory as the linear scalar field, the stress energy tensor is a renormalized quantity. Let us explain this briefly, using the example of the minimally coupled linear scalar field, following the path largely developed by Wald [@Wald78; @WaldQFTCST]. On any spacetime, the classical minimally coupled linear scalar field $\phi$ obeys the field equation $$\label{waveeqn}
\nabla^a\nabla_a\phi + m^2\phi = 0 \,.$$ The stress energy tensor for a classical solution $\phi$ of the field equation can be presented in the form $$T_{ab}(x) = \lim_{y \to x} P_{ab}(x,y;\nabla_{(x)},\nabla_{(y)})\phi(x)\phi(y)$$ (where $x,y$ are points in spacetime) with some partial differential operator $P_{ab}(x,y;\nabla_{(x)},\nabla_{(y)})$. This serves as starting point for defining ${\sf T}_{\boldsymbol{M}ab}$ through replacing $\phi$ by the quantized linear scalar field $\Phi_{\boldsymbol{M}}$. However, one finds already in Minkowski spacetime that upon performing this replacement, the behaviour of the resulting expression is singular in the coincidence limit $y \to x$. As usual with non-linear expressions in a quantum field at coinciding points, one must prescribe a renormalization procedure 