Towards a gauge theory for evolution equations on vector-valued spaces
| Autor: | Cardanobile, Stefano, Mugnolo, Delio |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | J.Math.Phys.50:103520,2009 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.3227666 |
| Popis: | We investigate symmetry properties of vector-valued diffusion and Schr\"odinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(\Omega, H)$ 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. Comment: 8 pages |
| Databáze: | arXiv |
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