The vector-ladder operators for the rotation group O3

1993 ◽  
Vol 71 (3-4) ◽  
pp. 152-154
Author(s):  
J. E. Hardy
Keyword(s):  
Rotation Group ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Straightforward Calculation ◽  
Angular Momenta ◽  
State Formula

The two vector-ladder operators, which step from any state [Formula: see text] in an irreducible multiplet in the space of product states of two commuting angular momenta, are defined and all their nonvanishing matrix elements are given, facilitating direct, straightforward calculation of the six nearby nonsibling states [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text].

scholarly journals Mass generation in QCD — Oscillating quarks and gluons

2014 ◽  
Vol 29 (21) ◽  
pp. 1444015
Author(s):  
Peter Minkowski
Keyword(s):  
Harmonic Oscillator ◽  
Gauge Boson ◽  
Rotation Group ◽  
Broken Symmetry ◽  
Mass Generation ◽  
Symmetry Classification ◽  
Angular Momenta ◽  
Comparable Level ◽  
Space Rotation

The present lecture is devoted to embedding the approximate genuine harmonic oscillator structure of valence [Formula: see text] mesons and in more detail the qqq configurations for u, d, s flavored baryons in QCD for three light flavors of quark. It includes notes, preparing the counting of "oscillatory modes of N fl = 3 light quarks, u, d, s in baryons," using the [Formula: see text] broken symmetry classification, extended to the harmonic oscillator symmetry of 3 paired oscillator modes. [Formula: see text] stands for the space rotation group generated by the sum of the 3 individual angular momenta of quarks in their c.m. system. The oscillator extension to valence gauge boson states is not yet developed to a comparable level.

Construction of nuclear potentials from phase shifts at different energies and angular momenta

1988 ◽  
Vol 66 (7) ◽  
pp. 618-621 ◽  
Author(s):  
M. A. Hooshyar ◽  
M. Razavy
Keyword(s):  
Inverse Problems ◽  
Approximate Method ◽  
Continued Fraction ◽  
Phase Shifts ◽  
Nuclear Potential ◽  
Matrix Elements ◽  
Fixed Energy ◽  
Angular Momenta ◽  
Partial Waves

This paper is concerned with an approximate method of construction of a central nuclear potential when [Formula: see text]-matrix elements or phase shifts for different partial waves are given at different energies. This is done by a generalization of the continued-fraction technique that was formulated for solving inverse problems at fixed energy.

scholarly journals Spin lattices, state transfer, and bivariate Krawtchouk polynomials

2015 ◽  
Vol 93 (9) ◽  
pp. 979-984 ◽  
Author(s):  
Vincent X. Genest ◽  
Hiroshi Miki ◽  
Luc Vinet ◽  
Alexei Zhedanov
Keyword(s):  
Three Dimensional ◽  
Rotation Group ◽  
Matrix Elements ◽  
Quantum State Transfer ◽  
Krawtchouk Polynomials ◽  
Triangular Domain ◽  
State Transfer ◽  
Exactly Solvable ◽  
Spin Lattices ◽  
Transfer Properties

The quantum state transfer properties of a class of two-dimensional spin lattices on a triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly solvable are identified. The exact solutions are expressed in terms of the bivariate Krawtchouk polynomials that arise as matrix elements of the unitary representations of the rotation group on the states of the three-dimensional harmonic oscillator.

Quasi-particles in atomic shell theory

1970 ◽  
Vol 315 (1520) ◽  
pp. 27-37 ◽  
Keyword(s):  
Shell Theory ◽  
Particle Creation ◽  
Rotation Group ◽  
Coupling Scheme ◽  
Matrix Elements ◽  
Spin Orientation ◽  
Quasi Particle ◽  
Quantum Numbers ◽  
Fractional Parentage ◽  
Electronic Configurations

A new scheme is described for defining and classifying the states of the electronic configurations l N . The spaces for which the spin orientation is either up or down are both factored into two parts. Each of these parts (distinguished by a symbol Ɵ) corresponds to the irreducible representatio n (½ ½ ... ½ ) of the rotation group R Ɵ (2 l +1). The generators for this group are constructed from quasi-particle creation and annihilation operators. The angular momentum quantum numbers l Ɵ arising from the decomposition of (½ ½ ... ½) into representations of R Ɵ (3) can be used to couple the four parts together. No ambiguities arise when l < 9, thereby giving a very satisfactory coupling scheme. No coefficients of fractional parentage (c. f. p.) are required in the calculation of matrix elements. Simple explanations are given for some null c. f. p. and for some repeated eigenvalues of an operator that had previously been used to classify the state s of g N .

EXOTIC REPRESENTATIONS OF THE ISOTROPIC HARMONIC OSCILLATOR

1998 ◽  
Vol 13 (19) ◽  
pp. 3347-3360
Author(s):  
LUIS J. BOYA ◽  
ERIC CHISOLM ◽  
S. M. MAHAJAN ◽  
E. C. G. SUDARSHAN
Keyword(s):  
Harmonic Oscillator ◽  
Rotation Group ◽  
Continuous Family ◽  
Ladder Operators ◽  
Standard Representation ◽  
Isotropic Harmonic Oscillator

We contruct and study a continuous family of representations of the N-dimensional isotropic harmonic oscillator (N≥2) which are not unitarily equivalent to the standard one. We explain why such representations exist and we investigate their simpler properties: the spectrum of the Hamiltonian (which contains nonstandard values), the form of the energy eigenfunctions, and their behavior under the ladder operators. Various symmetry and dynamical groups (e.g. the rotation group) which are valid on the standard representation are not implemented on the new ones. We comment very briefly on the prospects of observing these representations experimentally.

Counting of oscillatory modes of valence quarks forming qqq baryons for three quark flavors u, d, s

2017 ◽  
Vol 32 (04) ◽  
pp. 1750004 ◽  
Author(s):  
Sonia Kabana ◽  
Peter Minkowski
Keyword(s):  
Field Theory ◽  
Finite Number ◽  
Center Of Mass ◽  
Rotation Group ◽  
Broken Symmetry ◽  
Mass System ◽  
Angular Momenta ◽  
Space Rotation ◽  
Three Space ◽  
Quark Flavors

We present the unique properties of oscillatory modes of [Formula: see text] light quarks — [Formula: see text], [Formula: see text], [Formula: see text] — using the [Formula: see text] broken symmetry classification. [Formula: see text] stands for the space rotation group generated by the sum of the three individual angular momenta of quarks in their c.m. system. The baryonic multiplets are shown to emerge from the picture of oscillating quarks in three space dimensions in the center-of-mass system of the baryons. All oscillatory modes are fully relativistic with a finite number of oscillators and this is forming the unique harmonic oscillator with these properties. The density of states as a function of mass-square is calculated. This estimate is of relevance for the accounting of the missing states of unobserved hadrons, as the here estimated baryonic multiplets include both the observed and the unobserved (or “missing”) hadrons. The estimate is conceptually different from Hagedorn’s model and is based on field theory of QCD.

Still another way to calculate representations of the three-dimensional pure rotation group

1967 ◽  
Vol 63 (2) ◽  
pp. 273-275 ◽  
Author(s):  
R. H. Albert
Keyword(s):  
Explicit Formula ◽  
Three Dimensional ◽  
Rotation Group ◽  
Matrix Elements ◽  
Irreducible Tensor ◽  
Pure Rotation ◽  
The Matrix ◽  
Finite Sum

AbstractAn explicit formula is derived for exp (iβJz) as a finite sum of irreducible tensor components. With this formula, a technique is developed to obtain the matrix elements of exp (iβJy).

scholarly journals Extraction of bare form factors for Bs →Kℓν decays in nonperturbative HQET

2019 ◽  
Vol 34 (28) ◽  
pp. 1950166
Author(s):  
Felix Bahr ◽  
Debasish Banerjee ◽  
Fabio Bernardoni ◽  
Mateusz Koren ◽  
Hubert Simma ◽  
...  
Keyword(s):  
Excited State ◽  
Correlation Functions ◽  
Form Factors ◽  
Matrix Elements ◽  
Final State ◽  
State Formula ◽  
Euclidean Lattice ◽  
Point Correlation ◽  
B Quark ◽  
Static Form

We discuss the extraction of the ground state [Formula: see text] matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical gauge-field ensembles with lattice spacings 0.075, 0.05 fm and pion masses 330, 270 MeV are used from the O[Formula: see text]-improved CLS 2-flavor simulations and the final state momentum is [Formula: see text] GeV. The b-quark is treated in HQET including the [Formula: see text] corrections. Fits to two-point and three-point correlation functions and suitable ratios including summed ratios are used, yielding consistent results with precision of around 2% which is not limited by the [Formula: see text] corrections but by the dominating static form factors. Excited state contributions are under reasonable control but are the bottleneck towards precision. We do not yet include a specific investigation of multi-hadron contaminations, a gap in the literature which ought to be filled soon.

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