共查询到20条相似文献,搜索用时 15 毫秒
1.
A unified method to construct the (multi-)boson realizations of the Lie and quantum algebras is proposed based on a universal deformation of boson (Heisenberg-Weyl) algebra and its multiboson realization. Some explicit examples, the Lie algebras sl(2) and su (Ill), q-boson algebra, quantum algebras sl(2)q and su (l,l)q, along with the q-ladder algebra are studied in detail. In particular, the square boson realizations of su (1,l) and su (l,l)q are naturally obtained as special cases. 相似文献
2.
Cyclic representations of quantum (super) algebras are studied at qp=1 using two methods:the quotient module method and the q-boson realization method.For the quantum algebras associated with any finite dimensional simple Lie algebra the general theory of two methods is given,and is generated to the quantum superalgebra Uqosp(1.2).By constructing the cyclic representation of q-Heisenberg-Wey1 superalgebras the q-boson realization method is generated to construction of cyclic representations of some high-rank quantum superalgebras. 相似文献
3.
Hong-chen FU 《理论物理通讯》1990,14(4):509-514
An inhomogeneous q-differential realization (q-IHDR) and its corresponding inhomogeneous q-boson realization (q-IHBR) of quantum group SU(n)q are studied. By making use of the q-IHBR a kind of infinite dimensional indecomposable and irreducible representations of SU(n)q is studied on the q-Fcck space. The finite dimensional irreducible representations of SU(n), are obtained on the finite dimensional subspaces of q-Fock space. As an example, these representations of SU(2)q are studied in detail and Jimbo standard irreducible representations are obtained. 相似文献
4.
Xu-Feng LIU 《理论物理通讯》1994,22(4):487-490
By means of the q-fermion and q-boson rea1ization methods some finite-dimensional irreducible representations of the quantum affine algebra Uq(sl2), in which the central element is represented as an arbitrary nonzero constant, are explicitly constructed when q is a root of unity. 相似文献
5.
By constructing a parametrized cyclic (PC) representation of the q-deformed Heisenberg-Weyl algebras the PC.represen tations of quan tum superalgebra Uqosp(l, 2n) are studied in terms of its q-boson realization. A new type of PC representations of the rank-1 quantum superalgebra Uqosp(l, 2) is obtained by this way. 相似文献
6.
We show that for q -1 there is no natural tensor product for q-differential algebras. In particular, the q-graded tensor product of q-differentials fails to satisfy the q-graded Leibniz rule. 相似文献
7.
In this paper we present a q-deformed osp(1, 2) superalgebra, construct a type of coherent state representations and obtain a q-differential realization for the q-deformed superalgebra.We also study some quantum optical properties of the q-deformed osp(1, 2) coherent states. 相似文献
8.
A. Lavagno A. M. Scarfone P. Narayana Swamy 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):351-354
On the basis of the quantum q-oscillator algebra in the
framework of quantum groups and non-commutative
q-differential calculus, we investigate a possible
q-deformation of the classical Poisson bracket in order
to extend a generalized q-deformed dynamics in the
classical regime. In this framework, classical q-deformed
kinetic equations, Kramers and Fokker-Planck equations, are
also studied. 相似文献
9.
W.-S. Chung 《International Journal of Theoretical Physics》2000,39(10):2407-2413
The multiboson realization of two-mode q-boson algebra with su
q (2) covarianceis constructed. A new quantum deformation of su(2) algebra is presented by useof this realization. 相似文献
10.
Sibasish Ghosh 《Czechoslovak Journal of Physics》1998,48(12):1517-1536
Forsu(1, 1)-symmetric Hamiltonians of quantum mechanical systems (e.g. single-mode quantum harmonic oscillator, radial Schrödinger equation for Coulomb problem or isotropic quantum harmonic oscillator, etc.), the Heisenberg algebra of phase-space variables in two dimensions satisfy the bilinear commutation relation [ip,x]=1 (in normal units). Also there are different realizations ofsu(1, 1) by the generators of quantum harmonic oscillator algebra. We seek here the forms of deformed Heisenberg algebras (bilinear in deformedx and ip) associated with deformedsu(1, 1)-symmetric Hamiltonians. These forms are not unique in contrast to the undeformed case; and these forms are obtained here by considering different realizations of the deformedsu(1, 1) algebra by deformed oscillator algebras (satisfying different bilinear relations in deformed creation and annihilation operators), and then imposing different conditions (e.g. the deformed Heisenberg algebra of the form of the undeformed one, the form of realizations of the deformedsu(1, 1) algebra by deformed phase-space variables being the same as that ofsu(1, 1) algebra by undeformed phase-space variables, etc.), assuming linear relations between deformed phase-space variables and deformed creation-annihilation operators (as it is done in the undeformed case), we get different Heisenberg algebras. These facts are revealed in the case of a two-body Calogero model in its centre of mass frame (and for no other integrable systems in one-dimension having potential of the formV(x i ? xj). 相似文献
11.
12.
GONG Renshan 《理论物理通讯》1997,28(2):231-236
By means of the k-order q-boson realizations of suq(1,1), a new kind of q-coherent states, the two-variable coherent states, are introduced for the quantum algebra suq(l,1).They are relative to a definite irreducible representation of suq(1,1) and shown to satisfy a completeness relation in a subspace of q-boson's Fock space. With the help of these coherent states the z-representation, representation in functional space, for suq(1,1) is also discussed. 相似文献
13.
Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules of the quantized enveloping algebras . On them the quantum Lie product is given by the quantum adjoint action.
Here we define for any finite-dimensional simple complex Lie algebra an abstract quantum Lie algebra independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete
quantum Lie algebras are isomorphic to an abstract quantum Lie algebra .
In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras associated to the same are isomorphic, 2) the quantum Lie product of any is q-antisymmetric. We also describe a construction of which establishes their existence.
Received: 23 May 1996 / Accepted: 17 October 1996 相似文献
14.
Run-Qiang Jian 《Letters in Mathematical Physics》2013,103(8):851-863
In this letter, we use quantum quasi-shuffle algebras to construct Rota–Baxter algebras, as well as tridendriform algebras. We also propose the notion of braided Rota–Baxter algebras, the relevant object of Rota–Baxter algebras in a braided tensor category. Examples of such new algebras are provided using quantum multi-brace algebras in a category of Yetter–Drinfeld modules. 相似文献
15.
Assuming the existence of the perfect crystal bases of Kirillov-Reshetikhin modules over simply-laced quantum affine algebras,
we construct certain perfect crystals for twisted quantum affine algebras, and also provide compelling evidence that the constructed
crystals are isomorphic to the conjectural crystal bases of Kirillov-Reshetikhin modules over twisted quantum affine algebras. 相似文献
16.
Denis Bernard 《Physics letters. [Part B]》1991,260(3-4):389-393
Quasi-triangular quantum Lie algebras are algebras of quantum Lie derivatives. We show how to associate a quasi-triangular quantum Lie algebra to any quantum group defined by exchange relations. This provides a systematical way for constructing bi-covariant differential calculus on exchange quantum groups. 相似文献
17.
Recently,there are two independent approaches related to a class of nonlinear Lie algebras of three generators;and the realizations of these generators are achieved respectively in Schwinger-boson and position representation.However,by use of the representation transformation between these two representations,the equivalence of the two realizations is therefore proved. 相似文献
18.
Drinfeld gave a current realization of the quantum affine algebras as a Hopf algebra with a simple comultiplication for the quantum current operators. In this Letter, we will present a generalization of such a realization of quantum Hopf algebras. As a special case, we will choose the structure functions for this algebra to be elliptic functions to derive certain elliptic quantum groups as a Hopf algebra, which degenerates into quantum affine algebras if we take certain degeneration of the structure functions. 相似文献
19.
Fermionic zero modes around non-abelian vortices are shown that they constitute two N = 2, d = 1 supersymmetric quantum mechanics algebras. These two algebras can be combined under certain circumstances to form a central charge extended N = 4 supersymmetric quantum algebra. We thoroughly discuss the implications of the existence of supersymmetric quantum mechanics algebras, in the quantum Hilbert space of the fermionic zero modes. 相似文献
20.
Haisheng Li 《Communications in Mathematical Physics》2011,308(3):703-741
We develop a theory of f{\phi} -coordinated (quasi-) modules for a general nonlocal vertex algebra where f{\phi} is what we call an associate of the one-dimensional additive formal group. By specializing f{\phi} to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of Li (Selecta Mathematica
(New Series) 11:349–397, 2005). As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum
vertex algebras and f{\phi} -coordinated modules to a certain quantum βγ-system explicitly. 相似文献