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Journal Cover Reviews in Mathematical Physics
  [SJR: 0.985]   [H-I: 32]   [0 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0129-055X - ISSN (Online) 1793-6659
   Published by World Scientific Homepage  [118 journals]
  • Continuity properties of the semi-group and its integral kernel in
           non-relativistic QED
    • Authors: Oliver Matte
      Abstract: Reviews in Mathematical Physics, Volume 28, Issue 05, June 2016.
      Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. Güneysu, J. S. Møller, and the present author, we study the continuity of the corresponding semi-group between weighted vector-valued [math]-spaces, continuity properties of elements in the range of the semi-group, and the pointwise continuity of an operator-valued semi-group kernel. We further discuss the continuous dependence of the semi-group and its integral kernel on model parameters. All these results are obtained for Kato decomposable electrostatic potentials and the actual assumptions on the model are general enough to cover the Nelson model as well. As a corollary, we obtain some new pointwise exponential decay and continuity results on elements of low-energetic spectral subspaces of atoms or molecules that also take spin into account. In a simpler situation where spin is neglected, we explain how to verify the joint continuity of positive ground state eigenvectors with respect to spatial coordinates and model parameters. There are no smallness assumptions imposed on any model parameter.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-07-15T09:01:45Z
      DOI: 10.1142/S0129055X16500112
  • Higher [math]-gerbe connections in geometric prequantization
    • Authors: Domenico Fiorenza, Christopher L. Rogers, Urs Schreiber
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant–Souriau [math]-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the [math]-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian [math]-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds, we find the [math]-algebra extension of Hamiltonian vector fields — which is the higher Poisson bracket of local observables — and show that it is equivalent to the construction proposed by the second author in [math]-plectic geometry. Finally, we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-07-21T09:34:09Z
      DOI: 10.1142/S0129055X16500124
  • Rellich’s theorem and [math]-body Schrödinger operators
    • Authors: K. Ito, E. Skibsted
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We show an optimal version of Rellich’s theorem for generalized [math]-body Schrödinger operators. It applies to singular potentials, in particular, to a model for atoms and molecules with infinite mass and finite extent nuclei. Our proof relies on a Mourre estimate [10] and a functional calculus localization technique.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-07-07T03:11:03Z
      DOI: 10.1142/S0129055X16500100
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