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224 results on '"Casimir operator"'

1. Visualization of light tetraquarks under the five-dimensional SU(2) representation.

Author

Bisht, Shuchi and Hothi, Navjot

Abstract

In this manuscript, a novel effort has been made to theoretically realize the construction of light tetraquarks made up of two quark-antiquark pairs using Lie group representation. It has been amiably shown that they constitute an isospin multiplet. A five-dimensional representation of the SU(2) group has been projected and these exotic hadrons innately fill this submission in the postulated SU(2) isospin group. Additionally, the attainment of isospin triplets and singlets of tetraquarks has also been done which satisfies the desired requirement of the Kronecker product of four doublets of the SU(2) group. Furthermore, the physical analysis of the states and the weights can be credibly given in terms of these light tetraquarks. [ABSTRACT FROM AUTHOR]

Published
2024
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2. Descriptions of strongly multiplicity free representations for simple Lie algebras.

Author

Sun, Bin-Ni and Zhao, Yufeng

Subjects
*LIE algebras, *MULTIPLICITY (Mathematics), *UNIVERSAL algebra, *ALGEBRA, *ENDOMORPHISMS, *ENDOMORPHISM rings
Abstract

Let g be a complex simple Lie algebra and Z (g) be the center of the universal enveloping algebra U (g). Denote by V λ the finite-dimensional irreducible g -module with highest weight λ. Lehrer and Zhang defined the notion of strongly multiplicity free representations for simple Lie algebras motivated by studying the structure of the endomorphism algebra End U (g) (V λ ⊗ r) in terms of the quotients of the Kohno's infinitesimal braid algebra. Kostant introduced the g -invariant endomorphism algebras R λ (g) = (End V λ ⊗ U (g)) g and R λ , π (g) = (End V λ ⊗ π (U (g))) g. In this paper, we give some other criteria for a multiplicity free representation to be strongly multiplicity free by classifying the pairs (g , V λ) , which are multiplicity free and for such pairs, R λ (g) and R λ , π (g) are generated by generalizations of the quadratic Casimir elements of Z (g). [ABSTRACT FROM AUTHOR]

Published
2024
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3. A Casimir operator for a Calogero W algebra.

Author

Correa, Francisco, Leal, Gonzalo, Lechtenfeld, Olaf, and Marquette, Ian

Subjects
*C*-algebras, *CENTER of mass, *ALGEBRA, *COMMUTATION (Electricity), *POLYNOMIALS
Abstract

We investigate the nonlinear algebra W 3 generated by the 9 functionally independent permutation-symmetric operators in the three-particle rational quantum Calogero model. Decoupling the center of mass, we pass to a smaller algebra W 3 ′ generated by 7 operators, which fall into a spin-1 and a spin- 3 2 representation of the conformal sl (2) subalgebra. The commutators of the spin- 3 2 generators with each other are quadratic in the spin-1 generators, with a central term depending on the Calogero coupling. One expects this algebra to feature three Casimir operators, and we construct the lowest one explicitly in terms of Weyl-ordered products of the 7 generators. It is a polynomial of degree 6 in these generators, with coefficients being up to quartic in ℏ and quadratic polynomials in the Calogero coupling ℏ 2 g (g − 1) . Putting back the center of mass, our Casimir operator for W 3 is a degree-9 polynomial in the 9 generators. The computations require the evaluation of nested Weyl orderings. The classical and free-particle limits are also given. Our scheme can be extended to any finite number N of Calogero particles and the corresponding nonlinear algebras WN and W N ′ . [ABSTRACT FROM AUTHOR]

Published
2024
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5. Algebraic structure of Dirac–Pauli equation with account to AMM of neutron in the presence of magnetic field with cylindrical symmetry.

Author

Seidi, Masoud

Subjects
*MAGNETIC fields, *LIE algebras, *MAGNETIC moments, *NEUTRONS, *OPERATOR algebras
Abstract

The eigenvalues and eigenfunctions of Dirac–Pauli equation have been obtained for a neutron with anomalous magnetic moment (AMM) in the presence of a strong magnetic field with cylindrical symmetry. In our calculations, the Nikiforov and Uvarov (NU) method has been used. Using the eigenfunctions and construction of the ladder operators, we show that these generators satisfy su(2) Lie algebra and computed the second-order Casimir operator of the lie algebra. [ABSTRACT FROM AUTHOR]

Published
2021
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6. Trace distance ergodicity for quantum Markov semigroups.

Author

Bertini, Lorenzo, De Sole, Alberto, and Posta, Gustavo

Abstract

We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral decomposition of the Lindblad generator. We then apply this criterion to the bosonic and fermionic Ornstein-Uhlenbeck semigroups and to a family of quantum Markov semigroups parametrized by semisimple Lie algebras and their irreducible representations, in which the Lindblad generator is given by the adjoint action of the Casimir element. [ABSTRACT FROM AUTHOR]

Published
2024
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8. The Molecular Super-Rotor

Author

Schmiedt, Hanno, Drake, Gordon W F, Editor-in-chief, Babb, James, Series editor, Bandrauk, Andre D., Series editor, Bartschat, Klaus, Series editor, Burke, Philip George, Series editor, Compton, Robert N, Series editor, Gallagher, Tom, Series editor, Joachain, Charles J., Series editor, Lambropoulos, Peter, Series editor, Leuchs, Gerd, Series editor, Meystre, Pierre, Series editor, and Schmiedt, Hanno

Published
2017
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9. Adjoint algebraic groups as automorphism groups of a projector on a central simple algebra.

Author

Petrov, Viktor A. and Semenov, Andrei V.

Subjects
*AUTOMORPHISM groups, *LINEAR algebraic groups, *ALGEBRA, *PROJECTORS
Abstract

We show that any adjoint absolutely simple linear algebraic group over a field of characteristic zero is the automorphism group of some projector on a central simple algebra. Projective homogeneous varieties can be described in these terms; in particular, we reproduce quadratic equations by Lichtenstein defining them. [ABSTRACT FROM AUTHOR]

Published
2020
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11. Application of the Gel'fand Matrix Method to the Missing Label Problem in Classical Kinematical Lie Algebras

Author

Campoamor-Stursberg, Rutwig and Campoamor-Stursberg, Rutwig

Abstract

We briefly review a matrix based method to compute the Casimir operators of Lie algebras, mainly certain type of contractions of simple Lie algebras. The versatility of the method is illustrated by constructing matrices whose characteristic polynomials provide the invariants of the kinematical algebras in (3+1)-dimensions. Moreover it is shown, also for kinematical algebras, how some reductions on these matrices are useful for determining the missing operators in the missing label problem (MLP)., UCM, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Published
2023

12. Casimir operators induced by the Maurer-Cartan equations

Author

Campoamor-Stursberg, Rutwig and Campoamor-Stursberg, Rutwig

Abstract

It is shown that for inhomogeneous Lie algebras having only one Casimir operator, the latter can be explicitly constructed from the Maurer-Cartan equations by means of wedge products. It is further proved that this constraint imposes sharp bounds for the dimension of the representation R defining the semidirect product. The procedure is generalized to compute also the rational invariant of some Lie algebras, M.E.C., U.C.M.-C.A.M., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Published
2023

13. Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators

Author

Campoamor-Stursberg, Rutwig, Low, S.G., Campoamor-Stursberg, Rutwig, and Low, S.G.

Abstract

Given a semidirect product g = s ⊎ r of semisimple Lie algebras s and solvable algebras r, we construct polynomial operators in the enveloping algebra U(g) of g that commute with r and transform like the generators of s, up to a functional factor that turns out to be a Casimir operator of r. Such operators are said to generate a virtual copy of s in U(g), and allow to compute the Casimir operators of g in closed form, using the classical formulae for the invariants of s. The behavior of virtual copies with respect to contractions of Lie algebras is analyzed. Applications to the class of Hamilton algebras and their inhomogeneous extensions are given., M.E.C, U.C.M.-C.A.M., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

Published
2023

15. Boson Realizations

Author

Iachello, Francesco, Englert, Berthold-Georg, Series editor, Hänggi, Peter, Series editor, Hillebrandt, Wolfgang, Series editor, Jones, Richard A L, Series editor, von Löhneysen, H., Series editor, Raimond, Jean-Michel, Series editor, Salmhofer, Manfred, Series editor, Theisen, Stefan, Series editor, Longair, Malcolm S., Series editor, Rubio, Angel, Series editor, Hjorth-Jensen, Morten, Series editor, Wells, James D., Series editor, Lewenstein, Maciej, Series editor, and Iachello, Francesco

Published
2015
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16. Basic Concepts

Author

Iachello, Francesco, Englert, Berthold-Georg, Series editor, Hänggi, Peter, Series editor, Hillebrandt, Wolfgang, Series editor, Jones, Richard A L, Series editor, von Löhneysen, H., Series editor, Raimond, Jean-Michel, Series editor, Salmhofer, Manfred, Series editor, Theisen, Stefan, Series editor, Longair, Malcolm S., Series editor, Rubio, Angel, Series editor, Hjorth-Jensen, Morten, Series editor, Wells, James D., Series editor, Lewenstein, Maciej, Series editor, and Iachello, Francesco

Published
2015
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17. Degeneracy Algebras and Dynamical Algebras

Author

Iachello, Francesco, Englert, Berthold-Georg, Series editor, Hänggi, Peter, Series editor, Hillebrandt, Wolfgang, Series editor, Jones, Richard A L, Series editor, von Löhneysen, H., Series editor, Raimond, Jean-Michel, Series editor, Salmhofer, Manfred, Series editor, Theisen, Stefan, Series editor, Longair, Malcolm S., Series editor, Rubio, Angel, Series editor, Hjorth-Jensen, Morten, Series editor, Wells, James D., Series editor, Lewenstein, Maciej, Series editor, and Iachello, Francesco

Published
2015
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18. Matrix Realizations

Author

Iachello, Francesco, Englert, Berthold-Georg, Series editor, Hänggi, Peter, Series editor, Hillebrandt, Wolfgang, Series editor, Jones, Richard A L, Series editor, von Löhneysen, H., Series editor, Raimond, Jean-Michel, Series editor, Salmhofer, Manfred, Series editor, Theisen, Stefan, Series editor, Longair, Malcolm S., Series editor, Rubio, Angel, Series editor, Hjorth-Jensen, Morten, Series editor, Wells, James D., Series editor, Lewenstein, Maciej, Series editor, and Iachello, Francesco

Published
2015
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20. SL 2(ℝ) as a Lie Group

Author

Godement, Roger, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Godement, Roger

Published
2015
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24. Hom-Lie triple systems with involution.

Author

Baklouti, Amir

Subjects
*LIE algebras
Abstract

In this work we we prove that all involutive Hom-Lie triple systems are whether simple or semi-simple. Moreover, we prove that an involutive simple Lie triple system give a rise of Involutive Hom-Lie triple system. [ABSTRACT FROM AUTHOR]

Published
2019
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25. On the Solution of the Schrödinger Equation with Position-Dependent Mass

Author

Mehmet Sezgin

Subjects
lie group, casimir operator, schrödinger equation, decomposition, Elementary particle physics, QC793-793.5
Abstract

We have considered the Iwasawa and Gauss decompositions for the Lie group SL(2,R). According to these decompositions, the Casimir operators of the group and the Hamiltonians with position-dependent mass were expressed. Then, the unbound state solutions of the Schrödinger equations with position-dependent mass were given.

Published
2020
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32. Supersymmetry in Nuclear Physics

Author

Frank, A., Van Isacker, P., Jolie, J., Höhler, Gerhard, editor, Fujimori, Atsushi, editor, Kühn, Johann H., editor, Varma, C., editor, Müller, Thomas, editor, Wülfle, Peter, editor, Steiner, Frank, editor, Trümper, Joachim, editor, Frank, A., Van Isacker, P., and Jolie, J.

Published
2009
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37. Quantum Hall Effect and Non-commutative Geometry

Author

Pasquier, Vincent, de Monvel, Anne Boutet, editor, Kaiser, Gerald, editor, Berry, M., editor, Berenstein, C., editor, Blanchard, P., editor, Fokas, A. S., editor, Sternheimer, D., editor, Tracy, C., editor, Rivasseau, Vincent, and Duplantier, Bertrand, editor

Published
2007
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39. Spectrum Generating Algebras and Dynamic Symmetries

Author

Iachello, Francesco, Beig, R., editor, Beiglböck, W., editor, Domcke, W., editor, Englert, B.-G., editor, Frisch, U., editor, Hänggi, P., editor, Hasinger, G., editor, Hepp, K., editor, Hillebrandt, W., editor, Imboden, D., editor, Jaffe, R. L., editor, Lipowsky, R., editor, Löhneysen, H. v., editor, Ojima, I., editor, Sornette, D., editor, Theisen, S., editor, Weise, W., editor, Wess, J., editor, Zittartz, J., editor, and Iachello, Francesco

Published
2006
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40. The Kähler Case

Author

Cachan, J.-M. Morel, editor, Groningen, F. Takens, editor, Paris, B. Teissier, editor, Habermann, Katharina, and Habermann, Lutz

Published
2006
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48. Kac-Moody Algebras

Author

Algebras, Kac-Moody, Bass, Hyman, editor, Oesterlé, Joseph, editor, Weinstein, Alan, editor, and Kumar, Shrawan

Published
2002
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