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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
  • 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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