scholarly journals The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres

2020 ◽  
Vol 53 (40) ◽  
pp. 405203
Author(s):  
Ş Kuru ◽  
I Marquette ◽  
J Negro
Keyword(s):  
Symmetry Algebra ◽  
Racah Algebra

scholarly journals Symmetry and unification from soft theorems and unitarity

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Clifford Cheung ◽  
Zander Moss
Keyword(s):  
Symmetry Algebra ◽  
Scalar Fields ◽  
Particle Interactions ◽  
Massive Scalar ◽  
Coset Space ◽  
Dimensional Theory ◽  
Finite Spectrum ◽  
Physical Constraints ◽  
High Energies ◽  
Zero Condition

Abstract We argue that symmetry and unification can emerge as byproducts of certain physical constraints on dynamical scattering. To accomplish this we parameterize a general Lorentz invariant, four-dimensional theory of massless and massive scalar fields coupled via arbitrary local interactions. Assuming perturbative unitarity and an Adler zero condition, we prove that any finite spectrum of massless and massive modes will necessarily unify at high energies into multiplets of a linearized symmetry. Certain generators of the symmetry algebra can be derived explicitly in terms of the spectrum and three-particle interactions. Furthermore, our assumptions imply that the coset space is symmetric.

Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case

2018 ◽  
Vol 24 (2) ◽  
pp. 175-183
Author(s):  
Jean-Claude Ndogmo
Keyword(s):  
Explicit Form ◽  
Nonlinear Equations ◽  
Variational Principles ◽  
Symmetry Algebra ◽  
First Integrals ◽  
Maximal Symmetry ◽  
General Order ◽  
Linear And Nonlinear ◽  
Variational Symmetries ◽  
Variational Symmetry

Abstract Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. A discussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations.

A Note on the Symmetry Algebra of An Asymmetric XXZ Quantum Spin Chain

1997 ◽  
Vol 11 (01) ◽  
pp. 17-24
Author(s):  
M. A. Rego-Monteiro
Keyword(s):  
Spin Chain ◽  
Symmetry Algebra ◽  
Quantum Spin ◽  
Quantum Spin Chain ◽  
Deformation Parameters ◽  
Surface Fields

We show that an interesting open asymmetric XXZ quantum spin chain with surface fields is invariant under a two-parametric generalization of the slq(2) algebra with deformation parameters being a particular root of unit.

scholarly journals Embeddings of the Racah Algebra into the Bannai-Ito Algebra

2015 ◽  
Author(s):  
Vincent X. Genest ◽  
◽  
Luc Vinet ◽  
Alexei Zhedanov ◽  
◽  
...  
Keyword(s):  
Racah Algebra

SYMMETRY IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (13) ◽  
pp. 2331-2346 ◽  
Author(s):  
KAI-WEN XU ◽  
CHUAN-JIE ZHU
Keyword(s):  
Light Cone ◽  
Integration Method ◽  
Symmetry Algebra ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Simple Interpretation ◽  
Brst Charge ◽  
Dimensional Gravity ◽  
Covariant Gauge ◽  
Liouville Action

We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL (2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl (2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

scholarly journals SUPERSYMMETRY AND THE DIRAC OSCILLATOR

1991 ◽  
Vol 06 (09) ◽  
pp. 1567-1589 ◽  
Author(s):  
C. QUESNE
Keyword(s):  
Ground State ◽  
Symmetry Algebra ◽  
Negative Energy ◽  
Dirac Oscillator ◽  
Relativistic Limit ◽  
First Order ◽  
Supersymmetric Partner ◽  
Negative Energy States ◽  
Pattern Characteristic ◽  
Supersymmetric Structure

We demonstrate the realization of supersymmetric quantum mechanics in the first-order Dirac oscillator equation by associating with it another Dirac equation, which may be considered as its supersymmetric partner. We show that both the particle and the antiparticle spectra, resulting from these two equations after filling the negative-energy states and redefining the physical ground state, indeed present the degeneracy pattern characteristic of unbroken supersymmetry. In addition, we analyze in detail two algebraic structures, each partially explaining the degeneracies present in the Dirac oscillator supersymmetric spectrum in the non-relativistic limit. One of them is the spectrum-generating superalgebra osp(2/2, ℝ), first proposed by Balantekin. We prove that it is closely connected with the supersymmetric structure of the first-order Dirac oscillator equation as its odd generators are the two sets of supercharges respectively associated with the equation and its supersymmetric partner. The other algebraic structure is an so(4)⊕so(3, 1) algebra, which is an extension of a similar algebra first considered by Moshinsky and Quesne. We prove that it is the symmetry algebra of the Dirac oscillator supersymmetric Hamiltonian. Some possible relations between the spectrum-generating superalgebra, the symmetry algebra, and their respective subalgebras are also suggested.

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