Towards a gauge theory for evolution equations on vector-valued spaces
Abstract
We investigate symmetry properties of vector-valued diffusion and Schr\"odinger equations. For a separable Hilbert space H we characterize the subspaces of L2(, H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.
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