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Reviews in Mathematical Physics
Journal Prestige (SJR): 0.808
Citation Impact (citeScore): 1
Number of Followers: 0  
  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]
  • Dirac operators with Lorentz scalar shell interactions
    • Authors: Markus Holzmann, Thomas Ourmières-Bonafos, Konstantin Pankrashkin
      Abstract: Reviews in Mathematical Physics, Volume 30, Issue 05, June 2018.
      This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions along the surface. After showing the self-adjointness of the resulting operator, we switch to the investigation of its spectral properties, in particular, to the existence and non-existence of eigenvalues. In the case of an attractive coupling, we study the eigenvalue asymptotics as the mass becomes large and show that the behavior of the individual eigenvalues and their total number are governed by an effective Schrödinger operator on the boundary with an external Yang–Mills potential and a curvature-induced potential.
      Citation: Reviews in Mathematical Physics
      PubDate: 2018-05-31T08:30:57Z
      DOI: 10.1142/S0129055X18500137
  • On the adiabatic theorem when eigenvalues dive into the continuum
    • Authors: H. D. Cornean, A. Jensen, H. K. Knörr, G. Nenciu
      Abstract: Reviews in Mathematical Physics, Volume 30, Issue 05, June 2018.
      We consider a reduced two-channel model of an atom consisting of a quantum dot coupled to an open scattering channel described by a three-dimensional Laplacian. We are interested in the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit. At the end of the paper, we present a short outlook on how our method may be extended to cover other classes of Hamiltonians; details will be given elsewhere.
      Citation: Reviews in Mathematical Physics
      PubDate: 2018-05-31T08:30:55Z
      DOI: 10.1142/S0129055X18500113
  • Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds
    • Authors: C. I. Lazaroiu, C. S. Shahbazi
      Abstract: Reviews in Mathematical Physics, Volume 30, Issue 05, June 2018.
      We give the global mathematical formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation when the duality structure of the Abelian gauge theory is described by a flat symplectic vector bundle [math] defined over the scalar manifold [math]. The construction uses a taming of [math], which we find to be the correct mathematical object globally encoding the inverse gauge couplings and theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of [math] to the bundle [math] and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over [math] and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows, in particular, that a generalization of part of the mathematical structure familiar from [math] supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.
      Citation: Reviews in Mathematical Physics
      PubDate: 2018-05-31T08:30:52Z
      DOI: 10.1142/S0129055X18500125
  • Erratum: Full regularity for a C*-algebra of the canonical commutation
    • Authors: Hendrik Grundling, Karl-Hermann Neeb
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      The proof of the main theorem of the paper [1] contains an error. We are grateful to Professor Ralf Meyer (Mathematisches Institut, Georg-August Universität Göttingen) for pointing out this mistake.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-08-29T06:27:34Z
      DOI: 10.1142/S0129055X17920027
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