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arXiv · 0902.3833

Towards a gauge theory for evolution equations on vector-valued spaces

Stefano Cardanobile·Delio Mugnolo
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Abstract

We investigate symmetry properties of vector-valued diffusion and Schrödinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(Ω, H)$ 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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Stefano Cardanobile, Delio Mugnolo. 2011-08-03. Towards a gauge theory for evolution equations on vector-valued spaces. https://doi.org/10.1063/1.3227666

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