1,150 research outputs found

    On invariants of graphs related to quantum sl(2)\mathfrak{sl}(2) at roots of unity

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    We show how to define invariants of graphs related to quantum sl(2)\mathfrak{sl}(2) when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions

    Lectures on quantization of gauge systems

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    A gauge system is a classical field theory where among the fields there are connections in a principal G-bundle over the space-time manifold and the classical action is either invariant or transforms appropriately with respect to the action of the gauge group. The lectures are focused on the path integral quantization of such systems. Here two main examples of gauge systems are Yang-Mills and Chern-Simons.Comment: 63 pages, 22 figures. Based on lectures given at the Summer School "New paths towards quantum gravity", Holbaek, Denmark, 200

    The Dirac operator and gamma matrices for quantum Minkowski spaces

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    Gamma matrices for quantum Minkowski spaces are found. The invariance of the corresponding Dirac operator is proven. We introduce momenta for spin 1/2 particles and get (in certain cases) formal solutions of the Dirac equation.Comment: 25 pages, LaTeX fil

    Quasitriangularity and enveloping algebras for inhomogeneous quantum groups

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    Coquasitriangular universal R{\cal R} matrices on quantum Lorentz and quantum Poincar\'e groups are classified. The results extend (under certain assumptions) to inhomogeneous quantum groups of [10]. Enveloping algebras on those objects are described.Comment: 18 pages, LaTeX file, minor change

    The algebraic Bethe ansatz for rational braid-monoid lattice models

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    In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_n and D_n Lie algebra and by the superalgebra Osp(n|2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvalues of the transfer matrix associated to the B_n, C_n, D_n, Osp(2n-1|2), Osp(2|2n-2), Osp(2n-2|2) and Osp(1|2n) models. The corresponding Bethe Ansatz equations can be formulated in terms of the root structure of the underlying algebra.Comment: plain latex, 48 pages, 1 figure (under request
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