Browsing by Author "Bimonte, G."

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    Bicovariant Calculus in Quantum Theory and a Generalization of the Gauss Law
    (2000-04-06) Bimonte, G.; Marmo, G.; Stern, Allen; University of Alabama Tuscaloosa
    We construct a deformation of the quantum algebra Fun(T* G). associated with Lie group G to the case where G is replaced by a quantum group Gq which has a bicovariant calculus. The deformation easily allows for the inclusion of the current algebra of left and right invariant one forms. We use it to examine a possible generalization of the Gauss law commutation relations for gauge theories based on Gq.
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    Hidden Quantum Group Structure in Einstein’s General Relativity
    (Elsevier, 1998-08-10) Bimonte, G.; Musto, R.; Stern, Allen; Vitale, P.; University of Alabama Tuscaloosa
    A new formal scheme is presented in which Einstein's classical theory of General Relativity appears as the common, invariant sector of a one-parameter family of different theories. This is achieved by replacing the Poincaré group of the ordinary tetrad formalism with a q-deformed Poincare group, the usual theory being recovered at q = 1. Although written in terms of non-commuting vierbein and spin-connection fields, each theory has the same metric sector leading to the ordinary Einstein-Hilbert action and to the corresponding equations of motion. The Christoffel symbols and the components of the Riemann tensor are ordinary commuting numbers and have the usual form in terms of a metric tensor built as an appropriate bilinear in the vierbeins. Furthermore, we exhibit a one-parameter family of Hamiltonian formalisms for general relativity, by showing that a canonical formalism a la Ashtekar can be built for any value of q. The constraints are still polynomial, but the Poisson brackets are not skewsymmetric for q ≠ 1.
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    SUq(2) Lattice Gauge Theory
    (1996-07-01) Bimonte, G.; Stern, Allen; Vitale, P.; University of Alabama Tuscaloosa
    We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, the symmetry gets promoted to a quantum group gauge symmetry. The theory depends on two parameters: the deformation parameter λ and the lattice spacing a. We show that the system of Kogut and Susskind is recovered when λ → 0, while QCD is recovered in the continuum limit (for any λ). We, thus, have the possibility of having a two-parameter regularization of QCD.