ar X iv : m at h - ph / 9 90 60 06 v 2 2 4 Ju l 1 99 9 Unitarily Equivalent Classes of First Order Differential Operators

ar X iv : m at h / 06 06 33 9 v 1 [ m at h . SP ] 1 4 Ju n 20 06 Eigenfunction expansions associated with 1 d periodic differential operators of order 2 n

We prove an explicit formula for the spectral expansions in L(R) generated by selfadjoint differential operators (−1) d dx2n + n−1

ar X iv : m at h - ph / 9 90 10 11 v 2 2 9 Ju n 19 99 NON - COMMUTATIVE BLOCH THEORY : AN OVERVIEW

For differential operators which are invariant under the action of an abelian group Bloch theory is the tool of choice to analyze spectral properties. By shedding some new non-commutative light on this we motivate the introduction of a noncommutative Bloch theory for elliptic operators on Hilbert C-modules. It relates properties of C-algebras to spectral properties of module operators such as b...

ar X iv : m at h - ph / 9 90 70 23 v 1 2 8 Ju l 1 99 9 EIGENFUNCTIONS , TRANSFER MATRICES , AND ABSOLUTELY CONTINUOUS SPECTRUM OF ONE - DIMENSIONAL SCHRÖDINGER OPERATORS

In this paper, we will primarily discuss one-dimensional discrete Schrödinger operators (hu)(n) = u(n + 1) + u(n − 1) + V (n)u(n) (1.1D) on ℓ 2 (Z) (and the half-line problem, h + , on ℓ 2 ({n ∈ Z | n > 0}) ≡ ℓ 2 (Z +)) with u(0) = 0 boundary conditions. We will also discuss the continuum analog (Hu)(x) = −u ′′ (x) + V (x)u(x) (1.1C) on L 2 (R) (and its half-line problem, H + , on L 2 (0, ∞) wi...

ar X iv : h ep - l at / 9 60 80 06 v 1 2 A ug 1 99

We study the order of the phase transition in the 3d U(1)+Higgs theory, which is the Ginzburg-Landau theory of superconductivity. We confirm that for small scalar self-coupling the transition is of first order. For large scalar self-coupling the transition ceases to be of first order, and a non-vanishing scalar mass suggests that the transition may even be of higher than second order.

ar X iv : n uc l - th / 9 90 60 29 v 3 1 5 Ju l 1 99 9 1 Quark Matter ’ 99 — Theoretical Summary : What Next ?