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4.15 Inhomogeneities

Allowing for inhomogeneities inevitably means taking a big step from finitely many degrees of freedom to infinitely many ones. There is no straightforward way to cut down the number of degrees of freedom to finitely many ones while being more general than in the homogeneous context. One possibility would be to introduce a small-scale cutoff such that only finitely many wave modes arise, e.g., through a lattice, as is indeed done in some coherent state constructions [269]. This is in fact expected to happen in a discrete framework such as quantum geometry, but would, at this stage of defining a model, simply be introduced by hand.

For the analysis of inhomogeneous situations there are several different approximation schemes:


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