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Journal Cover Reviews in Mathematical Physics
  [SJR: 1.092]   [H-I: 36]   [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]
  • [math]-algebra models and higher Chern–Simons theories
    • Authors: Patricia Ritter, Christian Sämann
      Abstract: Reviews in Mathematical Physics, Volume 28, Issue 09, October 2016.
      We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern–Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of [math]-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu–Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie [math]-algebra extensions of [math]. Finally, we study a number of [math]-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-10-07T04:18:25Z
      DOI: 10.1142/S0129055X16500215
  • Edge states at phase boundaries and their stability
    • Authors: M. Asorey, A. P. Balachandran, J. M. Pérez-Pardo
      Abstract: Reviews in Mathematical Physics, Volume 28, Issue 09, October 2016.
      We analyze the effects of Robin-like boundary conditions on different quantum field theories of spin 0, 1/2 and 1 on manifolds with boundaries. In particular, we show that these conditions often lead to the appearance of edge states. These states play a significant role in physical phenomena like quantum Hall effect and topological insulators. We prove in a rigorous way the existence of spectral lower bounds on the kinetic term of different Hamiltonians, even in the case of Abelian gauge fields where it is a non-elliptic differential operator. This guarantees the stability and consistency of massive field theories with masses larger than the lower bound of the kinetic term. Moreover, we find an upper bound for the deepest edge state. In the case of Abelian gauge theories, we analyze a generalization of Robin boundary conditions. For Dirac fermions, we analyze the cases of Atiyah–Patodi–Singer and chiral bag boundary conditions. The explicit dependence of the bounds on the boundary conditions and the size of the system is derived under general assumptions.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-10-07T04:18:23Z
      DOI: 10.1142/S0129055X16500203
  • Stability of gas measures under perturbations and discretizations
    • Authors: Roberto Fernández, Pablo Groisman, Santiago Saglietti
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      For a general class of gas models — which includes discrete and continuous Gibbsian models as well as contour or polymer ensembles — we determine a diluteness condition that implies: (1) uniqueness of the infinite-volume equilibrium measure; (2) stability of this measure under perturbations of parameters and discretization schemes, and (3) existence of a coupled perfect-simulation scheme for the infinite-volume measure together with its perturbations and discretizations. Some of these results have previously been obtained through methods based on cluster expansions. In contrast, our treatment is purely probabilistic and its diluteness condition is weaker than existing convergence conditions for cluster expansions.
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-10-04T09:28:48Z
      DOI: 10.1142/S0129055X16500227
  • Quantization and superselection sectors III: Multiply connected spaces and
           indistinguishable particles
    • Authors: N. P. (Klaas) Landsman
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We reconsider the (non-relativistic) quantum theory of indistinguishable particles on the basis of Rieffel’s notion of [math]-algebraic (“strict”) deformation quantization. Using this formalism, we relate the operator approach of Messiah and Greenberg (1964) to the configuration space approach pioneered by Souriau (1967), Laidlaw and DeWitt-Morette (1971), Leinaas and Myrheim (1977), and others. In dimension [math], the former yields bosons, fermions, and paraparticles, whereas the latter seems to leave room for bosons and fermions only, apparently contradicting the operator approach as far as the admissibility of parastatistics is concerned. To resolve this, we first prove that in [math] the topologically non-trivial configuration spaces of the second approach are quantized by the algebras of observables of the first. Secondly, we show that the irreducible representations of the latter may be realized by vector bundle constructions, among which the line bundles recover the results of the second approach. Mathematically speaking, representations on higher-dimensional bundles (which define parastatistics) cannot be excluded, which render the configuration space approach incomplete. Physically, however, we show that the corresponding particle states may always be realized in terms of bosons and/or fermions with an unobserved internal degree of freedom (although based on non-relativistic quantum mechanics, this conclusion is analogous to the rigorous results of the Doplicher–Haag–Roberts analysis in algebraic quantum field theory, as well as to the heuristic arguments which led Gell-Mann and others to qcd (i.e. Quantum Chromodynamics)).
      Citation: Reviews in Mathematical Physics
      PubDate: 2016-09-14T06:08:44Z
      DOI: 10.1142/S0129055X16500197
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