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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]
  • Integrability and vesture for harmonic maps into symmetric spaces
    • Authors: Shabnam Beheshti, Shadi Tahvildar-Zadeh
      Abstract: Reviews in Mathematical Physics, Volume 28, Issue 03, April 2016.
      After formulating the notion of integrability for axially symmetric harmonic maps from [math] into symmetric spaces, we give a complete and rigorous proof that, subject to some mild restrictions on the target, all such maps are integrable. Furthermore, we prove that a variant of the inverse scattering method, called vesture (dressing) can always be used to generate new solutions for the harmonic map equations starting from any given solution. In particular, we show that the problem of finding [math]-solitonic harmonic maps into a non-compact Grassmann manifold [math] is completely reducible via the vesture (dressing) method to a problem in linear algebra which we prove is solvable in general. We illustrate this method, and establish its agreement with previously known special cases, by explicitly computing a 1-solitonic harmonic map for the two cases [math] and [math] and showing that the family of solutions obtained in each case contains respectively the Kerr family of solutions to the Einstein vacuum equations, and the Kerr–Newman family of solutions to the Einstein–Maxwell equations in the hyperextreme sector of the corresponding parameters.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-05-11T02:37:21Z
      DOI: 10.1142/S0129055X16500069
  • A mathematical analysis of the [math] method for computing electronic
           excited energies of molecules
    • Abstract: Reviews in Mathematical Physics, Ahead of Print.
      This article is concerned with the GW method for finite electronic systems. In the first step, we provide a mathematical framework for the usual one-body operators that appear naturally in many-body perturbation theory. We then give a rigorous mathematical formulation of the [math] equations, and study the well-posedness of these equations, proving the existence of a unique solution in a perturbative regime.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-06-16T08:50:06Z
      DOI: 10.1142/S0129055X16500082
  • Covariant mutually unbiased bases
    • Authors: Claudio Carmeli, Jussi Schultz, Alessandro Toigo
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      The connection between maximal sets of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space and finite phase-space geometries is well known. In this article, we classify MUBs according to their degree of covariance with respect to the natural symmetries of a finite phase-space, which are the group of its affine symplectic transformations. We prove that there exist maximal sets of MUBs that are covariant with respect to the full group only in odd prime-power dimensional spaces, and in this case, their equivalence class is actually unique. Despite this limitation, we show that in dimension [math] covariance can still be achieved by restricting to proper subgroups of the symplectic group, that constitute the finite analogues of the oscillator group. For these subgroups, we explicitly construct the unitary operators yielding the covariance.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-06-10T04:07:00Z
      DOI: 10.1142/S0129055X16500094
  • A family of inequivalent Weyl representations of canonical commutation
           relations with applications to quantum field theory
    • Authors: Asao Arai
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We consider a family of irreducible Weyl representations of canonical commutation relations with infinite degrees of freedom on the abstract boson Fock space over a complex Hilbert space. Theorems on equivalence or inequivalence of the representations are established. As a simple application of one of these theorems, the well-known inequivalence of the time-zero field and conjugate momentum for different masses in a quantum scalar field theory is rederived with space dimension [math] arbitrary. Also a generalization of representations of the time-zero field and conjugate momentum is presented. Comparison is made with a quantum scalar field in a bounded region in [math]. It is shown that, in the case of a bounded space region with [math], the representations for different masses turn out to be mutually equivalent.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-05-27T05:52:34Z
      DOI: 10.1142/S0129055X16500070
  • Schwartz operators
    • Authors: M. Keyl, J. Kiukas, R. F. Werner
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      In this paper, we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them, in particular, with a number of different (but equivalent) families of seminorms which turns the space of Schwartz operators into a Fréchet space. The study of the topological dual leads to non-commutative tempered distributions which are discussed in detail as well. We show, in particular, that the latter can be identified with a certain class of quadratic forms, therefore making operations like products with bounded (and also some unbounded) operators and quantum harmonic analysis available to objects which are otherwise too singular for being a Hilbert space operator. Finally, we show how the new methods can be applied by studying operator moment problems and convergence properties of fluctuation operators.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-04-05T06:40:11Z
      DOI: 10.1142/S0129055X16300016
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