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1.
In this article we present explicit formulae for q-integration on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. Furthermore, our formulae can be regarded as a generalization of Jacksons q-integral to three or four dimensions and provide a new possibility for an integration over the whole space being invariant under translations and rotations.Received: 9 September 2003, Published online: 26 November 2003 相似文献
2.
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The calculations are based on the covariant differential calculus of these quantum spaces. Furthermore, our formulae can be regarded as a generalization of Jacksons q-derivative to three and four dimensions.Received: 26 September 2002, Revised: 18 June 2003, Published online: 2 October 2003 相似文献
3.
D. Mikulovic A. Schmidt H. Wachter 《The European Physical Journal C - Particles and Fields》2006,45(2):529-544
Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional
quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski space. For each case standard techniques for dealing with q-deformed Grassmann variables are developed. Formulae for multiplying supernumbers are given. The actions of symmetry generators
and fermionic derivatives upon antisymmetrized quantum spaces are calculated. The complete Hopf structure for all types of
quantum space generators is written down. From the formulae for the coproduct a realization of the L-matrices in terms of symmetry generators can be read off. The L-matrices together with the action of symmetry generators determine how quantum spaces of different type have to be fused
together.
Arrival of the final proofs: 6 December 2005 相似文献
4.
J.-z. Zhang 《The European Physical Journal C - Particles and Fields》2003,28(3):389-393
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators.
There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians; one originates from the perturbation expansion of the potential in one configuration space, the
other one originates from the perturbation expansion of the kinetic energy in another configuration space. In order to establish
a general foundation of the q-perturbation theory, two perturbation equivalence theorems are proved. The first is Equivalence Theorem I: Perturbation expressions
of the q-deformed uncertainty relations calculated by two pairs of undeformed operators are the same, and the two q-deformed uncertainty relations undercut Heisenberg's minimal one in the same style. The general Equivalence Theorem II is:
for any potential (regular or singular) the expectation values of two q-perturbation Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent to all orders of the perturbation
expansion. As an example of singular potentials the perturbation energy spectra of the q-deformed Coulomb potential are studied.
Received: 6 September 2002 / Revised version: 21 October 2002 / Published online: 14 April 2003
RID="a"
ID="a" e-mail: jzzhang@physik.uni-kl.de, jzzhang@ecust.edu.cn 相似文献
5.
We propose a q-deformed model of anharmonic vibrations in diatomic molecules. We study the applicability of the model to the phenomenological Dunham expansion by comparison with experimental data. In contrast with other applications where it is difficult to find a physical interpretation for the deformation parameter, q, in our analysis it is directly related to the third-order coefficient in the Dunham expansion. We study the consistency of the parameters that determine the q-deformed system by comparing them with the vibrational terms fitted to 161 electronic states of diatomic molecules. We show how to include both positive and negative anharmonicities in a simple and systematic way.Received: 16 July 2004, Published online: 24 August 2004PACS:
33.15.Mt Rotation, vibration, and vibration-rotation constants - 02.20.Uw Quantum groups - 31.15.Hz Group theory - 03.65.Fd Algebraic methods - 02.20.-a Group theoryV.K. Dobrev: Permanent address, and after 30 April 2004: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria 相似文献
6.
H. Wachter M. Wohlgenannt 《The European Physical Journal C - Particles and Fields》2002,23(4):761-767
In this paper we present explicit formulas for the *-product on quantum spaces which are of particular importance in physics,
i.e., the q-deformed Minkowski space and the q-deformed Euclidean space in 3 and 4 dimensions, respectively. Our formulas are complete and formulated using the deformation
parameter q. In addition, we worked out an expansion in powers of up to second order, for all considered cases.
Received: 6 June 2001 / Published online: 15 March 2002 相似文献
7.
Sebastian de Haro Sanjaye Ramgoolam Alessandro Torrielli 《Communications in Mathematical Physics》2007,273(2):317-355
We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace
functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played
by q-deformed Schur-Weyl duality of quantum groups. The appearance of Euler characters of configuration spaces of Riemann surfaces
in the expansion persists. We discuss the geometrical meaning of these formulae. 相似文献
8.
《Journal of Nonlinear Mathematical Physics》2013,20(3):333-347
Abstract A method is proposed in this paper to construct a new extended q-deformed KP (q-KP) hiearchy and its Lax representation. This new extended q-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its two kinds of reductions give the q-deformed Gelfand-Dickey hierarchy with self-consistent sources and the constrained q-deformed KP hierarchy, which include two types of q-deformed KdV equation with sources and two types of q-deformed Boussinesq equation with sources. All of these results reduce to the classical ones when q goes to 1. This provides a general way to construct (2+1)- and (1+1)-dimensional q-deformed soliton equations with sources and their Lax representations. 相似文献
9.
The solutions of the q-deformed equations of quantum conformal Weyl gravity in terms of q-deformed plane waves are given.
The text was submitted by the authors in English. 相似文献
10.
In the present paper we show that the Lorentz algebra as defined in [5] is isomorphic to an algebra closely related to a q-deformed algebra. On this algebra we define a Hopf algebra structure and show its action on q-spinor modules. This algebra is related to the q-deformed Minkowski space algebra by a non invertible factorisation.
Received: 12 June 1998 / Published online: 5 October 1998 相似文献
11.
Within the framework of the q-deformed Heisenberg algebra a dynamical equation of q-deformed quantum mechanics is discussed. The perturbative aspects of the q-deformed Schr?dinger equation are analyzed. General representations of the additional momentum-dependent interaction originating
from the q-deformed effects are presented in two approaches. As examples, such additional interactions related to the harmonic-oscillator
potential and the Morse potential are demonstrated.
Received: 26 February 2001 / Published online: 11 May 2001 相似文献
12.
S. Kharchev D. Lebedev M. Semenov-Tian-Shansky 《Communications in Mathematical Physics》2002,225(3):573-609
The paper deals with the analytic theory of the quantum q-deformed Toda chains; the technique used combines the methods of representation theory and the Quantum Inverse Scattering
Method. The key phenomenon which is under scrutiny is the role of the modular duality concept (first discovered by L. Faddeev)
in the representation theory of noncompact semisimple quantum groups. Explicit formulae for the Whittaker vectors are presented
in terms of the double sine functions and the wave functions of the N-particle q-deformed open Toda chain are given as a multiple integral of the Mellin–Barnes type. For the periodic chain the two dual
Baxter equations are derived.
Received: 11 April 2001 / Accepted: 8 October 2001 相似文献
13.
In this paper we shall introduce two q-analogues of the squeezed states in terms of the technique of integration within an ordered product of operators and the
properties of the inverses of q-deformed annihilation and creation operators, and some nonclassical properties of the states are examined. Furthermore, we
obtain some new completeness relations composed of the bra and ket which are not mutually Hermitian conjugate.
PACS numbers: 03.65.-w; 45.50.Ct.
Work supported by the National Natural Science Foundation of China under Grant 10574060 and the Natural Science Foundation
of Shandong Province of China under Grant Y2004A09. 相似文献
14.
Abdullah Algin 《Czechoslovak Journal of Physics》2002,52(9):1011-1019
A two-parameter deformed N = 2 SUSY algebra is constructed by using the q-deformed bosonic and fermionic Newton oscillator algebras. The Fock space representation of the (q
1,q
2)-deformed N = 2 SUSY algebra is analyzed. The comparison between the algebra constructed and earlier versions of deformed N = 2 SUSY algebras is also made. 相似文献
15.
D. Galetti J. T. Lunardi B. M. Pimentel M. Ruzzi 《International Journal of Theoretical Physics》2002,41(9):1673-1687
A study of the reducibility of the Fock space representation of the q-deformed harmonic oscillator algebra for real and root of unity values of the deformation parameter is carried out by using the properties of the Gauss polynomials. When the deformation parameter is a root of unity, an interesting result comes out in the form of a reducibility scheme for the space representation which is based on the classification of the primitive or nonprimitive character of the deformation parameter. An application is carried out for a q-deformed harmonic oscillator Hamiltonian, to which the reducibility scheme is explicitly applied.On leave from 相似文献
16.
The quantum group IGL
q
(N), the inhomogenization of GL
q
(N), is formulated with
-matrices. Theq-deformed universal enveloping algebra is constructed as the algebra of regular functionals in this formulation and contains the partial derivatives of the covariant differential calculus on the quantum space. 相似文献
17.
Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies
Jipeng Cheng 《Journal of Nonlinear Mathematical Physics》2017,24(1):7-19
The Miura and anti-Miura transformations between the q-deformed KP and the q-deformed modified KP hierarchies are investigated in this paper. Then the auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies are constructed through the combinations of the Miura and anti-Miura transformations. And the corresponding results are also generalized to the constrained cases. At last, some examples of Miura and auto-Backlund transformations are given. 相似文献
18.
Hebecker A. Schreckenberg S. Schwenk J. Weich W. Wess J. 《Zeitschrift fur Physik C Particles and Fields》1994,64(2):355-359
We extend the symmetric operators of theq-deformed Heisenberg algebra to essentially self-adjoint operators. On the extended domains the product of the operators is not defined. To represent the algebra we had to enlarge the representation and we find a Hilbert space representation of the deformed Heisenberg algebra in terms of essentially self-adjoint operators. The respective diagonalization can be achieved by aq-deformed Fourier transformation. 相似文献
19.
Ye-jun Xu Jun Song Hong-yi Fan Qiu-yu Liu 《International Journal of Theoretical Physics》2011,50(3):744-751
By virtue of deformation quantization methods we introduce the q-deformed coordinate representation. A new set of completeness and orthogonality relations composed of the ket and bra which
are not mutually Hermitian conjugates are derived. Further, using the eigenket and eigenbra for q-deformed coordinate some important quantum gate operators for continuum variables are realized and their properties are discussed. 相似文献
20.
The differences among quon operators, q
a-math oscillator operators and q-deformed oscillator operators are pointed out. The q-deformed ocsillator and q
a-math oscillator are constructed in terms of q
q = 0 quon. 相似文献