9,786 research outputs found

    Optimally defined Racah-Casimir operators for su(n) and their eigenvalues for various classes of representations

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    This paper deals with the striking fact that there is an essentially canonical path from the ii-th Lie algebra cohomology cocycle, i=1,2,...li=1,2,... l, of a simple compact Lie algebra \g of rank ll to the definition of its primitive Casimir operators C(i)C^{(i)} of order mim_i. Thus one obtains a complete set of Racah-Casimir operators C(i)C^{(i)} for each \g and nothing else. The paper then goes on to develop a general formula for the eigenvalue c(i)c^{(i)} of each C(i)C^{(i)} valid for any representation of \g, and thereby to relate c(i)c^{(i)} to a suitably defined generalised Dynkin index. The form of the formula for c(i)c^{(i)} for su(n)su(n) is known sufficiently explicitly to make clear some interesting and important features. For the purposes of illustration, detailed results are displayed for some classes of representation of su(n)su(n), including all the fundamental ones and the adjoint representation.Comment: Latex, 16 page

    Observationally-Motivated Analysis of Simulated Galaxies

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    The spatial and temporal relationships between stellar age, kinematics, and chemistry are a fundamental tool for uncovering the physics driving galaxy formation and evolution. Observationally, these trends are derived using carefully selected samples isolated via the application of appropriate magnitude, colour, and gravity selection functions of individual stars; conversely, the analysis of chemodynamical simulations of galaxies has traditionally been restricted to the age, metallicity, and kinematics of `composite' stellar particles comprised of open cluster-mass simple stellar populations. As we enter the Gaia era, it is crucial that this approach changes, with simulations confronting data in a manner which better mimics the methodology employed by observers. Here, we use the \textsc{SynCMD} synthetic stellar populations tool to analyse the metallicity distribution function of a Milky Way-like simulated galaxy, employing an apparent magnitude plus gravity selection function similar to that employed by the RAdial Velocity Experiment (RAVE); we compare such an observationally-motivated approach with that traditionally adopted - i.e., spatial cuts alone - in order to illustrate the point that how one analyses a simulation can be, in some cases, just as important as the underlying sub-grid physics employed.Comment: Accepted for publication in PoS (Proceedings of Science): Nuclei in the Cosmos XIII (Debrecen, Jul 2014); 6 pages; 3 figure

    Geometrical foundations of fractional supersymmetry

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    A deformed qq-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a qq-deformed boson. The limit of this algebra when qq is a nn-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge QQ and covariant derivative DD encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Berezin integral and fractional superspace measure arise as a natural part of our formalism. When qq is a root of unity the algebra is found to have a non-trivial Hopf structure, extending that associated with the anyonic line. One-dimensional ordinary/fractional superspace is identified with the braided line when qq is a root of unity, so that one-dimensional ordinary/fractional supersymmetry can be viewed as invariance under translation along this line. In our construction of fractional supersymmetry the qq-deformed bosons play a role exactly analogous to that of the fermions in the familiar supersymmetric case.Comment: 42 pages, LaTeX. To appear in Int. J. Mod. Phys.
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