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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]
  • Asymptotic behavior of zero mass spin 2 fields propagating in Kerr
    • Authors: Giulio Caciotta, Tiziana Raparelli
      Abstract: Reviews in Mathematical Physics, Volume 28, Issue 06, July 2016.
      We introduce [math], the inhomogeneous equation suitable to describe the solution of the linearized version of the conformal part of the Riemann tensor connected to the perturbations of the Kerr spacetime far from the origin. Then we find the right decays we have to impose to the source term [math] to obtain the peeling decays for this linearized solution. We explain how these decays are compatible with the ones we need to attack the full nonlinear problem following the Christodoulou–Klainerman approach, see [7, 11]. This result is expressed explicitly in Theorem 1.1 and requires some new detailed estimates for the connection coefficients related to the null cone foliation in Kerr, see [10], which could be considered as a useful result by itself.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-08-10T07:52:39Z
      DOI: 10.1142/S0129055X16500136
  • Semiclassical analysis for a Schrödinger operator with a U(2) artificial
           gauge: The periodic case
    • Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We consider a Schrödinger operator with a Hermitian [math] matrix-valued potential which is lattice-periodic and can be diagonalized smoothly on the whole [math] In the case of the potential taking its minimum only on the lattice, we prove that the well-known semiclassical asymptotics of the first band spectrum for a scalar potential remains valid for our model.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-08-03T03:18:24Z
      DOI: 10.1142/S0129055X16500148
  • 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
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