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Displaying 21 – 40 of 56

Generating series and asymptotics of classical spin networks

Francesco Costantino, Julien Marché (2015)

Journal of the European Mathematical Society

We study classical spin networks with group SU $_{2}$ . In the first part, using Gaussian integrals, we compute their generating series in the case where the edges are equipped with holonomies; this generalizes Westbury’s formula. In the second part, we use an integral formula for the square of the spin network and perform stationary phase approximation under some non-degeneracy hypothesis. This gives a precise asymptotic behavior when the labels are rescaled by a constant going to infinity.

Integrable models of interaction of matter with radiation.

Inozemtsev, Vladimir I., Inozemtseva, Natalia G. (2006)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Integrable string models in terms of chiral invariants of $S U (n), S O (n), S P (n)$ groups.

Gershun, Victor D. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Internal Symmetries and Additional Quantum Numbers for Nanoparticles

V.G. Yarzhemsky (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Wavefunctions of symmetrical nanoparticles are considered making use of induced representation method. It is shown that when, at the same total symmetry, the order of local symmetry group decreases, additional quantum numbers are required for complete labelling of electron states. It is shown that the labels of irreducible representations of intermediate subgroups can be used for complete classification of states in the case of repeating IRs in symmetry adapted linear combinations. The intermediate...

Invariant symbolic calculus for compact Lie groups

Benjamin Cahen (2019)

Archivum Mathematicum

We study the invariant symbolic calculi associated with the unitary irreducible representations of a compact Lie group.

Invariant symbolic calculus for semidirect products

Benjamin Cahen (2018)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be the semidirect product $V ⋊ K$ where $K$ is a connected semisimple non-compact Lie group acting linearly on a finite-dimensional real vector space $V$ . Let $π$ be a unitary irreducible representation of $G$ which is associated by the Kirillov-Kostant method of orbits with a coadjoint orbit of $G$ whose little group is a maximal compact subgroup of $K$ . We construct an invariant symbolic calculus for $π$ , under some technical hypothesis. We give some examples including the Poincaré group.

Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator

Eugen Paal, Jüri Virkepu (2011)

Banach Center Publications

Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of three-dimensional real Lie algebras. The Jacobi operators of these quantum algebras are explicitly calculated.

Kreĭn spaces in de Sitter quantum theories.

Gazeau, Jean-Pierre, Siegl, Petr, Youssef, Ahmed (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Models of quadratic algebras generated by superintegrable systems in 2D.

Post, Sarah (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Modular symmetry and fractional charges in $𝒩 = 2$ supersymmetric Yang-Mills and the quantum Hall effect.

Dolan, Brian P. (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

New representations of the Poincaré group describing two interacting bosons

E. Frochaux (1999)

Annales de l'I.H.P. Physique théorique

On Nambu bracket representations of 3-algebras.

Şochichiu, Corneliu (2009)

APPS. Applied Sciences

On parametrization of the linear $GL (4, ℂ)$ and unitary $SU (4)$ groups in terms of Dirac matrices.

Red'kov, Victor M., Bogush, Andrei A., Tokarevskaya, Natalia G. (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

On quantum de Rham cohomology theory.

Cao, Huai-Dong, Zhou, Jian (1999)

Electronic Research Announcements of the American Mathematical Society [electronic only]

On the contraction of the discrete series of $S U (1, 1)$

C. Cishahayo, S. De Bièvre (1993)

Annales de l'institut Fourier

It is shown, using techniques inspired by the method of orbits, that each non-zero mass, positive energy representation of the Poincaré group $𝒫^{1, 1} = S O (1, 1) \otimes_{s} ℝ^{2}$ can be obtained via contraction from the discrete series of representations of $S U (1, 1)$ .

On the uniqueness of the $(2, 2)$ -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.

Peniche, R., Sánchez-Valenzuela, O.A., Thompson, F. (2004)

International Journal of Mathematics and Mathematical Sciences

Currently displaying 21 – 40 of 56

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Displaying 21 – 40 of 56

Generating series and asymptotics of classical spin networks

Integrable models of interaction of matter with radiation.

Integrable string models in terms of chiral invariants of $S U (n), S O (n), S P (n)$ groups.

Internal Symmetries and Additional Quantum Numbers for Nanoparticles

Invariant symbolic calculus for compact Lie groups

Invariant symbolic calculus for semidirect products

Jacobi operators of quantum counterparts of three-dimensional real Lie algebras over the harmonic oscillator

Kreĭn spaces in de Sitter quantum theories.

Models of quadratic algebras generated by superintegrable systems in 2D.

Modular symmetry and fractional charges in $𝒩 = 2$ supersymmetric Yang-Mills and the quantum Hall effect.

New representations of the Poincaré group describing two interacting bosons

On Nambu bracket representations of 3-algebras.

On parametrization of the linear $GL (4, ℂ)$ and unitary $SU (4)$ groups in terms of Dirac matrices.

On quantum de Rham cohomology theory.

On the contraction of the discrete series of $S U (1, 1)$

On the uniqueness of the $(2, 2)$ -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.

Ordering of energy levels for extended $S U (N)$ Hubbard chain.

Polarization and Unitary Representations of Solvable Lie Groups.

Quantum entanglement and projective ring geometry.

Quantum spacetime

Currently displaying 21 – 40 of 56