ar X iv : m at h - ph / 0 20 70 25 v 1 1 9 Ju l 2 00 2 Bound states due to a strong δ interaction supported by a curved surface

ar X iv : m at h - ph / 0 20 70 25 v 2 1 4 N ov 2 00 2 Bound states due to a strong δ interaction supported by a curved surface

We study the Schrödinger operator −∆ − αδ(x − Γ) in L 2 (R 3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion...

ar X iv : m at h - ph / 0 30 30 72 v 1 3 1 M ar 2 00 3 Eigenvalue asymptotics for the Schrödinger operator with a δ - interaction on a punctured surface

Given n ≥ 2, we put r = min{ i ∈ N; i > n/2 }. Let Σ be a compact, Cr-smooth surface in Rn which contains the origin. Let further {Sǫ}0≤ǫ<η be a family of measurable subsets of Σ such that supx∈Sǫ |x| = O(ǫ) as ǫ → 0. We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator −∆−βδ(·−Σ\Sǫ) in L2(Rn), where β is a positive constant, as ǫ → 0. An analogous result is g...

ar X iv : m at h - ph / 0 20 30 28 v 1 1 8 M ar 2 00 2 Curvature - induced bound states for a δ interaction supported by a curve in R 3

We study the Laplacian in L 2 (R 3) perturbed on an infinite curve Γ by a δ interaction defined through boundary conditions which relate the corresponding generalized boundary values. We show that if Γ is smooth and not a straight line but it is asymptotically straight in a suitable sense, and if the interaction does not vary along the curve, the perturbed operator has at least one isolated eig...

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : m at h - ph / 0 10 70 21 v 1 2 0 Ju l 2 00 1 Enlarged geometries of gauge bundles

The geometrical picture of gauge theories must be enlarged when a gauge potential ceases to behave like a connection, as it does in electroweak interactions. When the gauge group has dimension four, the vector space isomorphism between spacetime and the gauge algebra is realized by a tetrad– like field. The object measuring the deviation from a strict bundle structure has the formal behavior of...