FINITE OSCILLATOR MODELS DESCRIBED BY THE LIE SUPERALGEBRA sl(2|1)
نویسنده
چکیده
The literature on quantum mechanics in a finite-dimensional Hilbert space is substantial. This paper is devoted to an algebraic model for a quantum oscillator allowing finite-dimensional representations, thus leading to a finite oscillator model. The canonical one-dimensional quantum oscillator (in the convention m = ω = ~ = 1) is described by a position operator q̂, a momentum operator p̂ and a Hamiltonian Ĥ given by
منابع مشابه
0 Classification of Infinite Dimensional Weight Modules over the Lie
We give a complete classification of infinite dimensional indecomposable weight modules over the Lie superalgebra sl(2/1). §1. Introduction Among the basic-classical Lie superalgebras classified by Kac [3], the lowest dimensional of these is the Lie superalgebra B(0, 1) or osp(1, 2), while the lowest dimensional of these which has an isotropic odd simple root is the Lie superalgebra A(1, 0) or ...
متن کاملBlocks of Lie Superalgebras of Type W(n)
Let g be a simple, finite-dimensional Lie superalgebra over C. These have been classified by V. Kac. Unless g is a Lie algebra or a Lie superalgebra of type osp(1, 2n), the category of finite-dimensional representations of g is not semisimple; q.v. [8]. This leads to a classification problem. For example, in [4], the representation theory of sl(m,n) is worked out by showing it is wild when m,n ...
متن کاملProof of Proposition 3
Let g be a simple, finite-dimensional Lie superalgebra over C. These have been classified by V. Kac. Unless g is a Lie algebra or a Lie superalgebra of type osp(1, 2n), the category of finite-dimensional representations of g is not semisimple; q.v. [6]. This leads to a classification problem. For example, in [3], the representation theory of sl(m,n) is worked out by showing it is wild when m,n ...
متن کاملRepresentations of the Exceptional Lie Superalgebra E(3, 6) Iii: Classification of Singular Vectors
We continue the study of irreducible representations of the exceptional Lie superalgebra E(3, 6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sl(3) × sl(2) × gl(1) as the zero degree component of its consistent Z-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3, 6), completi...
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 کامل