scholarly journals Some results on the eigenfunctions of the quantum trigonometric Calogero–Sutherland model related to the Lie algebra E6

2005 ◽  
Vol 46 (7) ◽  
pp. 073508 ◽  
Author(s):  
J. Fernández Núñez ◽  
W. García Fuertes ◽  
A. M. Perelomov
Keyword(s):  
Lie Algebra ◽  
Sutherland Model

scholarly journals Some results on the eigenfunctions of the quantum trigonometric Calogero–Sutherland model related to the Lie algebra D4

2003 ◽  
Vol 44 (11) ◽  
pp. 4957-4974 ◽  
Author(s):  
J. Fernández Núñez ◽  
W. Garcı́a Fuertes ◽  
A. M. Perelomov
Keyword(s):  
Lie Algebra ◽  
Sutherland Model

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Reduction of partially invariant submodels of rank 3 defect 1 to invariant submodels

2018 ◽  
Vol 13 (3) ◽  
pp. 59-63 ◽  
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Gas Dynamics ◽  
Hydrodynamic Type ◽  
System Of Equations ◽  
Two Dimensional ◽  
Equations Of Gas Dynamics ◽  
Entropy Functions

Equations of hydrodynamic type with the equation of state in the form of pressure separated into a sum of density and entropy functions are considered. Such a system of equations admits a twelve-dimensional Lie algebra. In the case of the equation of state of the general form, the equations of gas dynamics admit an eleven-dimensional Lie algebra. For both Lie algebras the optimal systems of non-similar subalgebras are constructed. In this paper two partially invariant submodels of rank 3 defect 1 are constructed for two-dimensional subalgebras of the twelve-dimensional Lie algebra. The reduction of the constructed submodels to invariant submodels of eleven-dimensional and twelve-dimensional Lie algebras is proved.

ε‎-Invariance

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Algebra ◽  
Lie Group

The discussions up to Chapter 4 have been concerned with the Lie group. In this chapter, the Lie algebra is constructed by defining the operators ∇ and ∇̃.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

2019 ◽  
Vol 1 (3) ◽  
Author(s):  
Alexander Wietek ◽  
Philippe Corboz ◽  
Stefan Wessel ◽  
B. Normand ◽  
Frédéric Mila ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Product Phase ◽  
Sutherland Model
Sign in / Sign up

Export Citation Format

Share Document