643 research outputs found

### SU3 isoscalar factors

A summary of the properties of the Wigner Clebsch-Gordan coefficients and
isoscalar factors for the group SU3 in the SU2$\otimes$U1 decomposition is
presented. The outer degeneracy problem is discussed in detail with a proof of
a conjecture (Braunschweig's) which has been the basis of previous work on the
SU3 coupling coefficients. Recursion relations obeyed by the SU3 isoscalar
factors are produced, along with an algorithm which allows numerical
determination of the factors from the recursion relations. The algorithm
produces isoscalar factors which share all the symmetry properties under
permutation of states and conjugation which are familiar from the SU2 case. The
full set of symmetry properties for the SU3 Wigner-Clebsch-Gordan coefficients
and isoscalar factors are displayed.Comment: 20 pages, LaTeX (earlier version incomplete

### Quarks in the Skyrme-'t Hooft-Witten Model

The three-flavor Skyrme-'t Hooft-Witten model is interpreted in terms of a
quark-like substructure, leading to a new model of explicitly confined
color-free ``quarks'' reminiscent of Gell-Mann's original pre-color quarks, but
with unexpected and significant differences.Comment: Latex, 6 pages, no figure

### Three Dimensional Quantum Geometry and Deformed Poincare Symmetry

We study a three dimensional non-commutative space emerging in the context of
three dimensional Euclidean quantum gravity. Our starting point is the
assumption that the isometry group is deformed to the Drinfeld double D(SU(2)).
We generalize to the deformed case the construction of the flat Euclidean space
as the quotient of its isometry group ISU(2) by SU(2). We show that the algebra
of functions becomes the non-commutative algebra of SU(2) distributions endowed
with the convolution product. This construction gives the action of ISU(2) on
the algebra and allows the determination of plane waves and coordinate
functions. In particular, we show that: (i) plane waves have bounded momenta;
(ii) to a given momentum are associated several SU(2) elements leading to an
effective description of an element in the algebra in terms of several physical
scalar fields; (iii) their product leads to a deformed addition rule of momenta
consistent with the bound on the spectrum. We generalize to the non-commutative
setting the local action for a scalar field. Finally, we obtain, using harmonic
analysis, another useful description of the algebra as the direct sum of the
algebra of matrices. The algebra of matrices inherits the action of ISU(2):
rotations leave the order of the matrices invariant whereas translations change
the order in a way we explicitly determine.Comment: latex, 37 page

### Influence of Coulomb distortion on polarization observables in elastic electromagnetic lepton hadron scattering at low energies

The formal expression for the most general polarization observable in elastic
electromagnetic lepton hadron scattering at low energies is derived for the
nonrelativistic regime. For the explicit evaluation the influence of Coulomb
distortion on various polarization observables is calculated in a distorted
wave Born approximation. Besides the hyperfine interaction also the spin-orbit
interactions of lepton and hadron are included. For like charges the Coulomb
repulsion reduces strongly the size of polarization observables compared to the
plane wave Born approximation whereas for opposite charges the Coulomb
attraction leads to a substantial increase of these observables for hadron lab
kinetic energies below about 20 keV.Comment: 32 pages, 26 figures. Typos corrected, notation slightly changed,
figures redrawn, one figure and references added. A condensed version is in
press in Physical Review

### The q-harmonic oscillators, q-coherent states and the q-symplecton

The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton

### Collective spontaneous emission in a q-deformed Dicke model

The q-deformation of a single quantized radiation mode interacting with a
collection of two level atoms is introduced, analysing its effects on the
cooperative behavior of the system.Comment: 11 pages, RevTeX file, 2 figures available from authors, accepted for
publication in Mod. Phys. Lett.

### Color Non-Singlet Spectroscopy

Study of the spectrum and structure of color non-singlet combinations of
quarks and antiquarks, neutralized by a non-dynamical compensating color
source, may provide an interesting way to address questions about QCD that
cannot be addressed by experiment at the present time. These states can be
simulated in lattice QCD and the results can be used to improve
phenomenological models of hadrons. Here these ideas are applied to color
triplet states of qqqq and qq bar q.Comment: References added and typos correcte

### Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,

A new approach to the theory of polynomial solutions of q - difference
equations is proposed. The approach is based on the representation theory of
simple Lie algebras and their q - deformations and is presented here for
U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of
n(n-1)/2 commuting variables and depending on n-1 complex representation
parameters r_i, is constructed. From this realization lowest weight modules
(LWM) are obtained which are studied in detail for the case n=3 (the well known
n=2 case is also recovered). All reducible LWM are found and the polynomial
bases of their invariant irreducible subrepresentations are explicitly given.
This also gives a classification of the quasi-exactly solvable operators in the
present setting. The invariant subspaces are obtained as solutions of certain
invariant q - difference equations, i.e., these are kernels of invariant q -
difference operators, which are also explicitly given. Such operators were not
used until now in the theory of polynomial solutions. Finally the states in all
subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files

### Quantum state swapping via qubit network with Hubbard interaction

We study the quantum state transfer (QST) in a class of qubit network with
on-site interaction, which is described by the generalized Hubbard model with
engineered couplings. It is proved that the system of two electrons with
opposite spins in this quantum network of $N$ sites can be rigorously reduced
into $N$ one dimensional engineered single Bloch electron models with central
potential barrier. With this observation we find that such system can perform a
perfect QST, the quantum swapping between two distant electrons with opposite
spins. Numerical results show such QST and the resonant-tunnelling for the
optimal on-site interaction strengths.Comment: 4 pages, 3 figure

### The Schwinger Representation of a Group: Concept and Applications

The concept of the Schwinger Representation of a finite or compact simple Lie
group is set up as a multiplicity-free direct sum of all the unitary
irreducible representations of the group. This is abstracted from the
properties of the Schwinger oscillator construction for SU(2), and its
relevance in several quantum mechanical contexts is highlighted. The Schwinger
representations for $SU(2), SO(3)$ and SU(n) for all $n$ are constructed via
specific carrier spaces and group actions. In the SU(2) case connections to the
oscillator construction and to Majorana's theorem on pure states for any spin
are worked out. The role of the Schwinger Representation in setting up the
Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group is
brought out.Comment: Latex, 17 page

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