On Representations of Lie Algebras of a Generalized Tavis-cummings Model
نویسنده
چکیده
Consider the Lie algebras Lr,t : [K1,K2] = sK3, [K3,K1] = rK1, [K3,K2] = −rK2, [K3,K4] = 0, [K4,K1] = −tK1, and [K4,K2] = tK2, subject to the physical conditions, K3 and K4 are real diagonal operators representing energy, K2 = K † 1, and the Hamiltonian H = ω1K3 + (ω1 + ω2)K4 + λ(t)(K1e−iφ +K2e) is a Hermitian operator. Matrix representations are discussed and faithful representations of least degree for Lr,t satisfying the physical requirements are given for appropriate values of r,s, t ∈ R.
منابع مشابه
Universal Central Extension of Current Superalgebras
Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras are very impo...
متن کاملOn generalized reduced representations of restricted Lie superalgebras in prime characteristic
Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملApproximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{ast}$-algebras
Using fixed point method, we prove some new stability results for Lie $(alpha,beta,gamma)$-derivations and Lie $C^{ast}$-algebra homomorphisms on Lie $C^{ast}$-algebras associated with the Euler-Lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...
متن کاملFixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras
In this paper, using fixed point method, we prove the generalized Hyers-Ulam stability of random homomorphisms in random $C^*$-algebras and random Lie $C^*$-algebras and of derivations on Non-Archimedean random C$^*$-algebras and Non-Archimedean random Lie C$^*$-algebras for the following $m$-variable additive functional equation: $$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...
متن کامل