 But Gomes (2021) effaces this distinction: he argues that a field formalism maintains separability, but only at the cost of dealing with gauge variant field variables. Once we restrict attention to the gauge-invariant quantities, the nonseparability illustrated above (using the holonomy variables) is restored. Moreover, he argues that only in a vacuum is nonseparability conditional on the topology of spacetime. In the presence of charged matter, there may be gauge-invariant quantities that cannot be decomposed into smaller patches, even for simply-connected regions. And this is easy to illustrate: suppose that, instead of the phase factor \(S(C)\), for a closed loop C, we write \(S(I)\) for an open segment I, that begins at point x and ends at point y. For a (Klein-Gordon) charged scalar field \(\varphi\) that vanishes everywhere except at small neighborhoods \(\nu_x, \nu_y\), of x and y, the function: