Abstract
VII.1 Notation and preliminaries
The following definitions will be very convenient in the sequel:
Definition VII.1.
a) Let \(E\rightarrow M\) be a smooth metric \(\mathbb{C}\)-vector bundle. Then a Borel section \(V :\;M \rightarrow \mathrm{End}(E)\;\mathrm{in}\;\mathrm{End}(E) \rightarrow M\) is called a potential on \(E\rightarrow M\), if one has \(V(x)\;=\;V(x)^* \;\mathrm{for\;all}\;x \in M \). Here, \(V(x)^*\) denotes the adjoint of the finite-dimensional linear operator36 \(V(x)\;: \;E_x \rightarrow E_x\) with respect to the fixed metric on \(E\rightarrow M\)
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Güneysu, B. (2017). Foundations of Covariant Schrödinger Semigroups. In: Covariant Schrödinger Semigroups on Riemannian Manifolds. Operator Theory: Advances and Applications, vol 264. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-68903-6_7
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DOI: https://doi.org/10.1007/978-3-319-68903-6_7
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