Toward a gauge theory for evolution equations on vector-valued spaces
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چکیده
We investigate symmetry properties of vector-valued diffusion and Schrödinger equations. For a separable Hilbert space H we characterize the subspaces of L2 R3 ;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. © 2009 American Institute of Physics. doi:10.1063/1.3227666
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تاریخ انتشار 2009