A separation property for magnetic Schrödinger operators on Riemannian manifolds
نویسندگان
چکیده
منابع مشابه
Number Operators for Riemannian Manifolds
The Dirac operator d+ δ on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L2μΩ, [A,A ] acts as multiplication by a positive constant on excited states if and only if the logarithm of the measure density of dμ satisfies a pair of equations. The equations are equivalent to the existence of a harmonic distance function on M . Under these c...
متن کاملUniformly Elliptic Operators on Riemannian Manifolds
Given a Riemannian manifold (M, g), we study the solutions of heat equations associated with second order differential operators in divergence form that are uniformly elliptic with respect to g . Typical examples of such operators are the Laplace operators of Riemannian structures which are quasi-isometric to g . We first prove some Poincare and Sobolev inequalities on geodesic balls. Then we u...
متن کاملDirac Operators as “annihilation Operators” on Riemannian Manifolds
The following two situations are shown to be equivalent. I. The commutation relation [A,A∗] = α holds on the span of excited states of the form (A∗)kζ. Here A is a Dirac operator acting in a weighted Hilbert space of sections of a Dirac bundle S over a Riemannian manifold M , ζ is a vacuum state, and α > 0 is a constant. II. There exists a scalar solution h on all of M to the simultaneous equat...
متن کاملTime-dependent Scattering Theory for Schrödinger Operators on Scattering Manifolds *
We construct a time-dependent scattering theory for Schrödinger operators on a manifold M with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form R×∂M , where ∂M is the boundary of M at infinity. We prove the existence and the completeness of the wave operators, and show that our scattering matrix is equivalent to th...
متن کاملA Geometry Preserving Kernel over Riemannian Manifolds
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2011
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2010.09.001