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

Journal Article · Thu Oct 15 00:00:00 EDT 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3227666· OSTI ID:21294402

Cardanobile, Stefano ^[1]; Mugnolo, Delio ^[2]

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1. Bernstein Center for Computational Neuroscience, Hansastrasse 9A, D-79104 Freiburg (Germany)
2. Institut fuer Analysis, Universitaet Ulm, Helmholtzstrasse 18, D-89081 Ulm (Germany)

We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};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.

• OSTI ID: 21294402
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 10; Other Information: DOI: 10.1063/1.3227666; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
GAUGE INVARIANCE
HILBERT SPACE
MATHEMATICAL EVOLUTION
SCHROEDINGER EQUATION
VECTORS