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

Abstract

We investigate symmetry properties of vector-valued diffusion and Schrödinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(\Omega ,H)$ 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.

8 pages

References in corpus (1)

• Well-Posedness and Symmetries of Strongly Coupled Network Equations

Cited by in corpus (1)

• Parabolic systems with coupled boundary conditions