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Combinatorial aspects of representations of U(n)

Description: The boson operator theory of the representations of the unitary group, its Wigner-Clebsch-Gordan, and Racah coefficients is reformulated in terms of the ring of polynomials in any number of indeterminates with the goal of bringing the theory, as nearly as possible, under the purview of combinatorial oriented concepts. Four of the basic relations in unitary group theory are interpreted from this viewpoint.
Date: December 31, 1996
Creator: Louck, J.D.
Partner: UNT Libraries Government Documents Department

A guide to flat direction analysis in anomalous U(1) models

Description: The authors suggest a systematic procedure to study D- and F-flat directions in a large class of models with an anomalous U(1). This class of models is characterized by the existence of a vacuum that breaks all Abelian gauge symmetries connecting the observable sector to the hidden sector. They show that, under some conditions, there is no other stable vacuum that breaks these symmetries. As a consequence, the model yields definite (order of magnitude) predictions for low-energy mass hierarchies. Then they study generic flat directions and identify the ones that may lead to undesirable vacua. They give necessary conditions for those to be lifted, and show that supersymmetry breaking only slightly affects the conclusions from the flat direction analysis.
Date: December 1, 1997
Creator: Irges, N. & Lavignac, S.
Partner: UNT Libraries Government Documents Department

On the anomalous U(1) in free fermionic superstring models

Description: The realistic free fermionic models have had an intriguing success in explaining different properties of the observed particle spectrum. In this paper the authors discuss in some detail the anomalous U(1) symmetry which exists in these models. They study the properties of the anomalous U(1) in both the more realistic NAHE-based free fermionic models and those in a general NAHE class. Appearance of an anomalous U(1) in the more realistic NAHE models is shown to be an effect of reduction of world-sheet supersymmetry from (2,2) to (2,0). They show, however, that in more general (2,1) and (2,0) models, all U(1) can remain anomaly-free under certain conditions. Several phenomenological issues related to the anomalous U(1) are discussed. In particular, they note that in some examples the anomalous U(1) arises from the breaking E{sub 6} {yields} SO(10) {times} U(1){sub A}, resulting in U(1){sub A} being family universal.
Date: November 1, 1997
Creator: Cleaver, G.B. & Faraggi, A.E.
Partner: UNT Libraries Government Documents Department

Combinatorics, geometry, and mathematical physics

Description: This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.
Date: November 1, 1998
Creator: Chen, W.Y.C. & Louck, J.D.
Partner: UNT Libraries Government Documents Department

Quantum groups, roots of unity and particles on quantized Anti-de Sitter space

Description: Quantum groups in general and the quantum Anti-de Sitter group U{sub q}(so(2,3)) in particular are studied from the point of view of quantum field theory. The author shows that if q is a suitable root of unity, there exist finite-dimensional, unitary representations corresponding to essentially all the classical one-particle representations with (half) integer spin, with the same structure at low energies as in the classical case. In the massless case for spin {ge} 1, {open_quotes}naive{close_quotes} representations are unitarizable only after factoring out a subspace of {open_quotes}pure gauges{close_quotes}, as classically. Unitary many-particle representations are defined, with the correct classical limit. Furthermore, the author identifies a remarkable element Q in the center of U{sub q}(g), which plays the role of a BRST operator in the case of U{sub q}(so(2,3)) at roots of unity, for any spin {ge} 1. The associated ghosts are an intrinsic part of the indecomposable representations. The author shows how to define an involution on algebras of creation and anihilation operators at roots of unity, in an example corresponding to non-identical particles. It is shown how nonabelian gauge fields appear naturally in this framework, without having to define connections on fiber bundles. Integration on Quantum Euclidean space and sphere and on Anti-de Sitter space is studied as well. The author gives a conjecture how Q can be used in general to analyze the structure of indecomposable representations, and to define a new, completely reducible associative (tensor) product of representations at roots of unity, which generalizes the standard {open_quotes}truncated{close_quotes} tensor product as well as many-particle representations.
Date: May 23, 1997
Creator: Steinacker, H.
Partner: UNT Libraries Government Documents Department

Unitary symmetry, combinatorics, and special functions

Description: From 1967 to 1994, Larry Biedenham and I collaborated on 35 papers on various aspects of the general unitary group, especially its unitary irreducible representations and Wigner-Clebsch-Gordan coefficients. In our studies to unveil comprehensible structures in this subject, we discovered several nice results in special functions and combinatorics. The more important of these will be presented and their present status reviewed.
Date: December 31, 1996
Creator: Louck, J.D.
Partner: UNT Libraries Government Documents Department

Massless and massive monopoles carrying nonabelian magnetic charges

Description: The properties of BPS monopoles carrying nonabelian magnetic charges are investigated by following the behavior of the moduli space of solutions as the Higgs field is varied from a value giving a purely abelian symmetry breaking to one that leaves a nonabelian subgroup of the gauge symmetry unbroken. As the limit of nonabelian unbroken symmetry is reached, some of the fundamental abelian monopoles remain massive but acquire nonabelian magnetic charges. The BPS mass formula indicates that others should because massless in this limit. These do not correspond to distinct solitons, but instead are manifested as a ``nonabelian cloud`` surrounding the massive monopoles, with their position and phase degrees of freedom being transformed into parameters characterizing the cloud.
Date: October 1, 1996
Creator: Weinberg, E.J.
Partner: UNT Libraries Government Documents Department

CP violation at CDF

Description: A major goal of experimental particle physics over the next decade is to measure the sides and angles of the Unitarity triangle redundantly, and as precisely as possible. Overconstraining the triangle will test the Cabbibo-Kobayashi-Maskawa model of quark mixing. The CDF collaboration, due to begin a second run in March 2001 with major upgrades to both the accelerator and the detector, will study the angle {beta} using B{sup 0} decays, the angle {gamma} using B{sup 0} and B{sub s}{sup 0} decays, and a side of the triangle through the observation of B{sub s}{sup 0}--{bar B}{sub s}{sup 0} mixing. Projected sensitivities are driven mostly by previous measurements using data from the first run. One highlight of the Run I B physics program is a measurement of the CP violating parameter sin 2{beta} = 0.79{sub {minus}0.44}{sup +0.41}, based on a tagged sample of 400 B{sup 0} decays in the mode B{sub 0}/{bar B}{sup 0} {r_arrow} J/{psi}K{sub s}{sup 0}. The technology of flavor tagging, used here as well as in numerous B{sup 0}-{bar B}{sup 0} mixing analyses in run I, is crucial and will be augmented in Run II with better particle identification capabilities. Exclusive all-hadronic final states will enter the data sample in Run II through a new displaced track trigger.
Date: April 16, 2001
Creator: Boudreau, J.
Partner: UNT Libraries Government Documents Department

A meson exchange model for the YN interaction

Description: We present a new model for the hyperon-nucleon (Lambda N, Sigma N) interaction, derived within the meson exchange framework. The model incorporates the standard one boson exchange contributions of the lowest pseudoscalar and vector meson multiplets with coupling constants fixed by SU(6) symmetry relations. In addition - as the main feature of the new model - the exchange of two correlated pions or kaons, both in the scalar-isoscalar (sigma) and vector-isovector (rho) channels, is included.
Date: September 1, 2001
Creator: Haidenbauer, J.; Melnitchouk, W. & Speth, J.
Partner: UNT Libraries Government Documents Department

Representations of the symmetric group as special cases of the boson polynomials in U(n)

Description: The set of all real, orthogonal irreps of S/sub n/ are realized explicitly and nonrecursively by specializing the boson polynomials carrying irreps of the unitary group. This realization makes use of a 'calculus of patterns', which is discussed.
Date: January 1, 1978
Creator: Biedenharn, L.C. & Louck, J.D.
Partner: UNT Libraries Government Documents Department

Nucleon-nucleon potentials and two-body Hamiltonians. [Bethe-Salpeter equation, two-nucleon mass operator]

Description: The physical significance of nucleon-nucleon potentials depends on their relation to the two-nucleon mass operator. These relations are examined for phenomenological potentials. Momentum space Bethe-Salpeter amplitudes with one particle on the mass shell approximate half-off-shell T matrices defined in the framework of the Haag-Ruelle theory. This implies a relation between potentials derived from a Bethe-Salpeter equation and effective two-body mass operators. 16 references.
Date: January 1, 1979
Creator: Coester, F
Partner: UNT Libraries Government Documents Department

Zero range three-particle equations. [Karlsson-Zeiger equations]

Description: In order to separate the entire effect of two-particle on-shell scatterings in three-particle systems from the effects of hidden mesonic degrees of freedom (off-shell effects and three-body forces), the zero range limit of the Karlsson-Zeiger equations. Although the Faddeev equations are ambiguous in this limit, the KZ equations remain well defined. Using only two-particle phase shifts, binding energies, and reduced widths, these zero-range equations uniquely predict the three-particle observables which would occur in the absence of hidden mesonic degrees of freedom. The three-particle amplitudes possess all requisite physical symmetry properties, and can be proved to be unitary if the spectator basis is orthonormal and complete. Possible extensions of the scheme for the analysis of three-particle final states, to zero range four-particle equations, and to relativistic systems are conjectured.
Date: April 1, 1978
Creator: Noyes, H.P. & Zeiger, E.M.
Partner: UNT Libraries Government Documents Department