ar X iv : m at h / 02 01 22 7 v 1 [ m at h . SP ] 2 3 Ja n 20 02 D - S PROJECTION METHODS FOR DISCRETE SCHRÖDINGER OPERATORS

ar X iv : m at h / 02 01 22 7 v 2 [ m at h . SP ] 1 3 Fe b 20 03 PROJECTION METHODS FOR DISCRETE SCHRÖDINGER OPERATORS

Let H be the discrete Schrödinger operator Hu(n) := u(n − 1) + u(n + 1) + v(n)u(n), u(0) = 0 acting on l(Z) where the potential v is real-valued and v(n) → 0 as n → ∞. Let P be the orthogonal projection onto a closed linear subspace L ⊂ l(Z). In a recent paper E.B. Davies defines the second order spectrum Spec2(H,L) of H relative to L as the set of z ∈ C such that the restriction to L of the op...

ar X iv : m at h - ph / 0 20 10 06 v 2 1 5 Ja n 20 02 Quasi - classical versus non - classical spectral asymptotics for magnetic Schrödinger operators with decreasing electric potentials

We consider the Schrödinger operator H on L 2 (R 2) or L 2 (R 3) with constant magnetic field, and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of the discrete spectrum of H near the boundary points of its essential spectrum. If the decay of V is Gaussian or faster, this behaviour is non-classical in...

ar X iv : m at h / 02 01 15 9 v 1 [ m at h . D G ] 1 7 Ja n 20 02 Reduction of HKT - Structures

KT-geometry is the geometry of a Hermitian connection whose torsion is a 3-form. HKT-geometry is the geometry of a hyper-Hermitian connection whose torsion is a 3-form. We identify non-trivial conditions for a reduction theory for these types of geometry.

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

ar X iv : h ep - t h / 02 01 09 7 v 1 1 5 Ja n 20 02 LORENTZ VIOLATION AT ONE LOOP

The proof of one-loop renormalizability of the general Lorentz-and CPT-violating extension of quantum electrodynamics is described. Application of the renormalization-group method is discussed and implications for theory and experiment are considered.