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Using distributions is a trick that people use whenever dealing with systems that do not have the required smoothness and integrability conditions and is in general only a mathematical technique to nevertheless solve those problems. Maxwell equations, to start with, require both sides to be differentiable (at least a few times) and integrable and when you ...


I am not at all an expert of quantum gravity, but I think you have misunderstood the point. As I understand it, the point is not necessarily having distributions as quantum Hilbert space vectors, but having a distributional "configuration space", i.e. distributions as the domain of the function(al)s that are the quantum vectors. While in QM (i.e. for ...

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