International Journal of Modern Physics A, ISSN 0217-751X, 04/2018, Volume 33, Issue 10, p. 1850055

We express each Clebsch–Gordan (CG) coefficient of a discrete group as a product of a CG coefficient of its subgroup and a factor, which we call an embedding...

Clebsch-Gordan coefficients | discrete groups | PSL(2, 7) | flavor symmetry | PSL(2,7) | PHYSICS, NUCLEAR | SYMMETRIC GAUGE-THEORIES | CP VIOLATION | PHYSICS, PARTICLES & FIELDS | Physics

Clebsch-Gordan coefficients | discrete groups | PSL(2, 7) | flavor symmetry | PSL(2,7) | PHYSICS, NUCLEAR | SYMMETRIC GAUGE-THEORIES | CP VIOLATION | PHYSICS, PARTICLES & FIELDS | Physics

Journal Article

Nuclear Physics, Section A, ISSN 0375-9474, 01/2016, Volume 945, pp. 144 - 152

It is argued that several papers where SU(3) Clebsch–Gordan coefficients were calculated in order to describe properties of hadronic systems are, up to a phase...

[formula omitted] Clebsch–Gordan coefficients | Large [formula omitted] QCD hadrons | Group theory | SU clebsch-gordan coefficients | QCD hadrons | Large N

[formula omitted] Clebsch–Gordan coefficients | Large [formula omitted] QCD hadrons | Group theory | SU clebsch-gordan coefficients | QCD hadrons | Large N

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 11/2017, Volume 2017, Issue 11, pp. 1 - 75

We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer...

Discrete Symmetries | AdS-CFT Correspondence | Gauge-gravity correspondence | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | 1/N Expansion | Elementary Particles, Quantum Field Theory | COMPLETE 1/N EXPANSION | CORRELATORS | YANG-MILLS THEORY | COMPLEXITY | QUANTUM-GRAVITY | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Clebsch-Gordan coefficients | Permutations | Sequences | Correlation | Group theory | Color | Correlators | Coefficients | Matrix methods | Mathematical models | Graphical representations | Symmetry

Discrete Symmetries | AdS-CFT Correspondence | Gauge-gravity correspondence | Quantum Physics | Quantum Field Theories, String Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | 1/N Expansion | Elementary Particles, Quantum Field Theory | COMPLETE 1/N EXPANSION | CORRELATORS | YANG-MILLS THEORY | COMPLEXITY | QUANTUM-GRAVITY | PHYSICS, PARTICLES & FIELDS | Analysis | Algebra | Clebsch-Gordan coefficients | Permutations | Sequences | Correlation | Group theory | Color | Correlators | Coefficients | Matrix methods | Mathematical models | Graphical representations | Symmetry

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 11/2017, Volume 193, Issue 2, pp. 1715 - 1724

Using properties of the Shannon and Tsallis entropies, we obtain new inequalities for the Clebsch–Gordan coefficients of the group SU(2). For this, we use...

information-entropic inequality | Tsallis entropy | Theoretical, Mathematical and Computational Physics | Wigner 3 j symbol | Shannon entropy | Applications of Mathematics | subadditivity condition | Clebsch–Gordan coefficient | Hahn polynomial | Physics | Wigner 3j symbol | Clebsch-Gordan coefficient | STATES | PHYSICS, MULTIDISCIPLINARY | QUDIT | PHYSICS, MATHEMATICAL | Distribution (Probability theory)

information-entropic inequality | Tsallis entropy | Theoretical, Mathematical and Computational Physics | Wigner 3 j symbol | Shannon entropy | Applications of Mathematics | subadditivity condition | Clebsch–Gordan coefficient | Hahn polynomial | Physics | Wigner 3j symbol | Clebsch-Gordan coefficient | STATES | PHYSICS, MULTIDISCIPLINARY | QUDIT | PHYSICS, MATHEMATICAL | Distribution (Probability theory)

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 11/2019, Volume 109, Issue 11, pp. 2485 - 2490

We present a new sum rule for Clebsch–Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is...

Geometry | 20C35 | 81R05 | Theoretical, Mathematical and Computational Physics | Complex Systems | 3 j symbols | 22E70 | Group Theory and Generalizations | Sum rules | Physics | Clebsch–Gordan coefficients

Geometry | 20C35 | 81R05 | Theoretical, Mathematical and Computational Physics | Complex Systems | 3 j symbols | 22E70 | Group Theory and Generalizations | Sum rules | Physics | Clebsch–Gordan coefficients

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 02/2016, Volume 49, Issue 11

Generating functions for Clebsch-Gordan coefficients of osp (1 vertical bar 2) are derived. These coefficients are expressed as q -> -1 limits of the dual...

Clebsch-Gordan coefficients | Dunkl oscillator | generating function | paraboson | Lie superalgebra osp(1|2) | Lie superalgebra osp (1 vertical bar 2) | POLYNOMIALS | ALGEBRA REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | LIE | PHYSICS, MATHEMATICAL | OPERATORS

Clebsch-Gordan coefficients | Dunkl oscillator | generating function | paraboson | Lie superalgebra osp(1|2) | Lie superalgebra osp (1 vertical bar 2) | POLYNOMIALS | ALGEBRA REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | LIE | PHYSICS, MATHEMATICAL | OPERATORS

Journal Article

1987, ISBN 9789971500726, vii, 230

Book

8.
Full Text
Construction of SO ( 5 ) ⊃ SO ( 3 ) spherical harmonics and Clebsch–Gordan coefficients

Computer Physics Communications, ISSN 0010-4655, 2009, Volume 180, Issue 7, pp. 1150 - 1163

The SO ( 5 ) ⊃ SO ( 3 ) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the...

[formula omitted] algebraic collective model | Spherical harmonics | Isoscalar factors | formula omitted | Bohr Hamiltonian | Clebsch–Gordan coefficients | Coupling coefficients | Clebsch-Gordan coefficients | SU (1, 1) × SO algebraic collective model

[formula omitted] algebraic collective model | Spherical harmonics | Isoscalar factors | formula omitted | Bohr Hamiltonian | Clebsch–Gordan coefficients | Coupling coefficients | Clebsch-Gordan coefficients | SU (1, 1) × SO algebraic collective model

Journal Article

Computer Physics Communications, ISSN 0010-4655, 07/2011, Volume 182, Issue 7, pp. 1543 - 1565

We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A–G based on the explicit construction...

Model building | Tensor product | GUT | Lie algebra | Multiple tensor product | Clebsch–Gordan coefficients | Tensor product decomposition | Symmetry breaking | Clebsch-Gordan coefficients | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | Algebra | Broken symmetry | Tensors | Computation | Mathematical analysis | Lie groups | Mathematical models | Representations

Model building | Tensor product | GUT | Lie algebra | Multiple tensor product | Clebsch–Gordan coefficients | Tensor product decomposition | Symmetry breaking | Clebsch-Gordan coefficients | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MATHEMATICAL | Algebra | Broken symmetry | Tensors | Computation | Mathematical analysis | Lie groups | Mathematical models | Representations

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2011, Volume 52, Issue 2

We present an algorithm for the explicit numerical calculation of SU(N) and SL(N, C) Clebsch-Gordan coefficients, based on the Gelfand-Tsetlin pattern...

SU3 | REPRESENTATIONS | SEMISIMPLE LIE GROUPS | PHYSICS, MATHEMATICAL | OPERATORS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | LIE GROUPS | SYMMETRY GROUPS | IMPLEMENTATION | COMPUTER CODES | SL GROUPS | ALGORITHMS | MATHEMATICAL LOGIC | MATHEMATICAL METHODS AND COMPUTING | CLEBSCH-GORDAN COEFFICIENTS | SU-2 GROUPS | SU GROUPS

SU3 | REPRESENTATIONS | SEMISIMPLE LIE GROUPS | PHYSICS, MATHEMATICAL | OPERATORS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | LIE GROUPS | SYMMETRY GROUPS | IMPLEMENTATION | COMPUTER CODES | SL GROUPS | ALGORITHMS | MATHEMATICAL LOGIC | MATHEMATICAL METHODS AND COMPUTING | CLEBSCH-GORDAN COEFFICIENTS | SU-2 GROUPS | SU GROUPS

Journal Article

General Relativity and Gravitation, ISSN 0001-7701, 4/2018, Volume 50, Issue 4, pp. 1 - 49

We compute transition amplitudes between two spin networks with dipole graphs, using the Lorentzian EPRL model with up to two (non-simplicial) vertices. We...

Loop quantum gravity | Spin foams | Theoretical, Mathematical and Computational Physics | SL(2, C) Clebsch–Gordan coefficients | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Physics | Astronomy, Astrophysics and Cosmology | MODELS | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | LOOP QUANTUM-GRAVITY | ASTRONOMY & ASTROPHYSICS | SL(2,C) Clebsch-Gordan coefficients | PHYSICS, PARTICLES & FIELDS | Analysis | Gravity

Loop quantum gravity | Spin foams | Theoretical, Mathematical and Computational Physics | SL(2, C) Clebsch–Gordan coefficients | Quantum Physics | Differential Geometry | Classical and Quantum Gravitation, Relativity Theory | Physics | Astronomy, Astrophysics and Cosmology | MODELS | PHYSICS, MULTIDISCIPLINARY | FIELD-THEORY | LOOP QUANTUM-GRAVITY | ASTRONOMY & ASTROPHYSICS | SL(2,C) Clebsch-Gordan coefficients | PHYSICS, PARTICLES & FIELDS | Analysis | Gravity

Journal Article

Journal of Theoretical and Computational Chemistry, ISSN 0219-6336, 04/2009, Volume 8, Issue 2, pp. 251 - 259

Using binomial coefficients, the new simple and efficient algorithms for the accurate and fast calculation of the Clebsch-Gordan and Gaunt coefficients, and...

Clebsch-Gordan coefficients | Gaunt coefficients | Gaussian type orbitals | Slater type orbitals | Wigner n - j symbols | STORAGE | ANGULAR-MOMENTUM COEFFICIENTS | CHEMISTRY, MULTIDISCIPLINARY | 3-J | SLATER-TYPE ORBITALS | ELECTRON-REPULSION INTEGRALS | PROGRAMS | SETS | 3N-J SYMBOLS | 6-J SYMBOLS | COMPUTATION

Clebsch-Gordan coefficients | Gaunt coefficients | Gaussian type orbitals | Slater type orbitals | Wigner n - j symbols | STORAGE | ANGULAR-MOMENTUM COEFFICIENTS | CHEMISTRY, MULTIDISCIPLINARY | 3-J | SLATER-TYPE ORBITALS | ELECTRON-REPULSION INTEGRALS | PROGRAMS | SETS | 3N-J SYMBOLS | 6-J SYMBOLS | COMPUTATION

Journal Article

15.
Full Text
A computer code for calculations in the algebraic collective model of the atomic nucleus

Computer Physics Communications, ISSN 0010-4655, 03/2016, Volume 200, pp. 220 - 253

A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which...

Algebraic collective model | Bohr model | SO Clebsch–Gordan coefficients | SO Clebsch-Gordan coefficients | STATES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTERACTING-BOSON MODEL | IBM | COEFFICIENTS | VERSION | SYSTEMS | LIMIT | PHYSICS, MATHEMATICAL | Clebsch-Gordan coefficients | Algebra | Computer simulation | Digits | Hilbert space | Mathematical models | Libraries | Nuclei

Algebraic collective model | Bohr model | SO Clebsch–Gordan coefficients | SO Clebsch-Gordan coefficients | STATES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INTERACTING-BOSON MODEL | IBM | COEFFICIENTS | VERSION | SYSTEMS | LIMIT | PHYSICS, MATHEMATICAL | Clebsch-Gordan coefficients | Algebra | Computer simulation | Digits | Hilbert space | Mathematical models | Libraries | Nuclei

Journal Article

Chemical Physics Letters, ISSN 0009-2614, 11/2019, Volume 735, p. 136769

•In the theoretical quantum mechanical studies, Gaunt coefficients are encountered.•Gaunt coefficients are associated with spherical harmonics.•Gaunt...

Clebsch-Gordan coefficients | Gaunt coefficients | Binomial coefficients | Bessel functions | Molecular integrals | SLATER-TYPE ORBITALS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | OVERLAP | CHEMISTRY, PHYSICAL | COULOMB INTEGRALS

Clebsch-Gordan coefficients | Gaunt coefficients | Binomial coefficients | Bessel functions | Molecular integrals | SLATER-TYPE ORBITALS | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | OVERLAP | CHEMISTRY, PHYSICAL | COULOMB INTEGRALS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 09/2010, Volume 51, Issue 9

A Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m/n). Explicit expressions for the...

ALGEBRAS | STATISTICS | Lie algebras | tensors | FINITE-DIMENSIONAL REPRESENTATIONS | PHYSICS, MATHEMATICAL | TSETLIN BASIS | PARA-BOSE

ALGEBRAS | STATISTICS | Lie algebras | tensors | FINITE-DIMENSIONAL REPRESENTATIONS | PHYSICS, MATHEMATICAL | TSETLIN BASIS | PARA-BOSE

Journal Article

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 01/2020, Volume 53, Issue 2, p. 25201

We discuss the construction and symmetries of su(3) Clebsch-Gordan coefficients arising from su(3) basis states constructed as triple tensor products of...

Clebsch-Gordan coefficients | PHYSICS, MULTIDISCIPLINARY | reflections | RACAH COEFFICIENTS | COUPLING-COEFFICIENTS | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS | WIGNER

Clebsch-Gordan coefficients | PHYSICS, MULTIDISCIPLINARY | reflections | RACAH COEFFICIENTS | COUPLING-COEFFICIENTS | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS | WIGNER

Journal Article

Annals of Physics, ISSN 0003-4916, 12/2012, Volume 327, Issue 12, pp. 2972 - 3047

A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of well-defined orthonormal local as...

Density matrix renormalization group | Tensor networks | Lie algebra | Non-abelian symmetries | Clebsch–Gordan coefficients | Numerical renormalization group | Clebsch-Gordan coefficients | ANDERSON | STATES | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | NUMERICAL RENORMALIZATION-GROUP | Analysis | Algebra | Algorithms | Quantum physics | Symmetry | Networks | Tensors | Mathematical analysis | Group theory | Charge | Mathematical models | Channels | U-1 GROUPS | TENSORS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | SU-3 GROUPS | ALGORITHMS | COMPARATIVE EVALUATIONS | CLEBSCH-GORDAN COEFFICIENTS | SU-2 GROUPS | DENSITY MATRIX | SP GROUPS | QUANTUM OPERATORS | QUANTUM FIELD THEORY | RENORMALIZATION

Density matrix renormalization group | Tensor networks | Lie algebra | Non-abelian symmetries | Clebsch–Gordan coefficients | Numerical renormalization group | Clebsch-Gordan coefficients | ANDERSON | STATES | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | NUMERICAL RENORMALIZATION-GROUP | Analysis | Algebra | Algorithms | Quantum physics | Symmetry | Networks | Tensors | Mathematical analysis | Group theory | Charge | Mathematical models | Channels | U-1 GROUPS | TENSORS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SPIN | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | ALGEBRA | SU-3 GROUPS | ALGORITHMS | COMPARATIVE EVALUATIONS | CLEBSCH-GORDAN COEFFICIENTS | SU-2 GROUPS | DENSITY MATRIX | SP GROUPS | QUANTUM OPERATORS | QUANTUM FIELD THEORY | RENORMALIZATION

Journal Article

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