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  • 1.
    Brack, M.
    et al.
    Institut für Theoretische Physik, Universität Regensburg, Regensburg, Germany.
    Ögren, Magnus
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Yu, Y.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Reimann, S. M.
    Division of Mathematical Physics, LTH, Lund University, Lund, Sweden.
    Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 46, p. 9941-9967Article in journal (Refereed)
    Abstract [en]

    We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term . This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term for small ε in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold which is covered by the parameters describing their four-fold degeneracy. Then, we obtain an analytical uniform trace formula for arbitrary ε which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit ε (or energy) →0 restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios ωrφ ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r4.

  • 2.
    Fjelstad, Jens
    Department of Physics, Nanjing University, Nanjing, China.
    On duality and extended chiral symmetry in the SL(2,R) WZW model2011In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 44, no 23, article id 235404Article in journal (Refereed)
    Abstract [en]

    Two chiral aspects of the SL(2,R) WZW model in an operator formalism are investigated. First, the meaning of duality, or conjugation, of primary fields is clarified. On a class of modules obtained from the discrete series it is shown, by looking at spaces of two-point conformal blocks, that a natural definition of contragredient module provides a suitable notion of conjugation of primary fields, consistent with known two-point functions. We find strong indications that an apparent contradiction with the Clebsch-Gordan series of SL(2,R), and proposed fusion rules, is explained by nonsemisimplicity of a certain category. Second, results indicating an infinite cyclic simple current group, corresponding to spectral flow automorphisms, are presented. In particular, the subgroup corresponding to even spectral flow provides part of a hypothetical extended chiral algebra resulting in proposed modular invariant bulk spectra.

  • 3.
    Fjelstad, Jens
    et al.
    Department of Physics, Nanjing University, Nanjing, China.
    Månsson, Teresia
    Department of Theoretical Physics, School of Engineering Sciences, Royal Institute of Technology (KTH), Stockholm, Sweden.
    New symmetries of the chiral Potts model2012In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 45, no 15, article id 155208Article in journal (Refereed)
    Abstract [en]

    In this paper a hithertho unknown symmetry of the three-state chiral Potts model is found consisting of two coupled Temperley-Lieb algebras. From these we can construct new superintegrable models. One realisation is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting charges. This leads us to a natural generalisation of the boost-operator, which generates the charges.

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