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1.
A realization of the Yangian double with center DYh(sl2)k of level-k(≠ 0, -2) in terms of free boson fields is constructed. The screening currents are also presented, which commute with DYh(sl2) modulo total difference. In the n → 0 limit, the currents of Yangian double DYh(sl2)k become the Feigin-Fuchs realization of affine Lie Sl(2)k, while the screening currents of Yangian double DYh(sl2)k become the screening currents of the affine Lie algebra sl(2)k. 相似文献
2.
B. Basu-Mallick 《Nuclear Physics B》1999,540(3):505-704
Here we construct some integrable Haldane-Shastry (HS) like spin chains, which exhibit multi-parameter deformed or non-standard variants of Y(glm) Yangian symmetry. By projecting the eigenstates of Dunkl operators in a suitable way, we also derive a class of exact eigenfunctions for such spin chains and subsequently conjecture that these exact eigenfunctions would lead to the highest weight states (HWS) associated with multi-parameter deformed or non-standard variants of Y(glM) Yangian algebra. By using this conjecture, and acting descendent operator on the HWS associated with a non-standard Y(gl2) Yangian algebra, we are able to find out the complete set of eigenvalues and eigenfunctions for the related HS-like
chain. It turns out that some additional energy levels, which are forbidden due to a selection rule in the case of SU(2) HS model, interestingly appear in the spectrum of the above mentioned HS-like spin chain with non-standard Y(gl2) symmetry. 相似文献
3.
We propose a rational quantum deformed nonlocal currentsin the homogeneous space SU(2)k/U(1),and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level k=c is obtained.In the classical limit h→0,the quantum nonlocal currents become SU(2)k parafermion,and the realization of Yangian double becomes the parafermion realization of SU(2)k current algebra. 相似文献
4.
《Nuclear Physics B》1998,527(3):657-689
Dimensional reduction of various gravity and supergravity models leads to effectively two-dimensional field theories described by gravity coupled G/H coset space σ-models. The transition matrices of the associated linear system provide a complete set of conserved charges. Their Poisson algebra is a semi-classical Yangian double modified by a twist which is a remnant of the underlying coset structure. The classical Geroch group is generated by the Lie-Poisson action of these charges. Canonical quantization of the structure leads to a twisted Yangian double with fixed central extension at a critical level. 相似文献
5.
Yangian代数是超出李代数更大的无穷维代数,是研究非线性量子完全可积系统的新对称特性的有力数学工具.基于介子态中夸克-味su(3)对称性和Yangian代数生成元的跃迁特性,本文研究了Yangian代数Y(su(3))生成元在三种正反介子态(π~±,K~±,K~0和K~0)各自组成的三种混合介子态(π,K和K_i~0)衰变中的作用.将Y(su(3))代数的八个生成元(I~±,U~±,V~±,I~3和I~8)作为跃迁算子,作用在混合介子态上,研究其可能的衰变道,以及衰变前后纠缠度的变化.结果表明:1)在李代数范围内的生成元I~3和I~8作用下,三种混合介子态衰变后组成成分没有发生变化,其中混合介子态π在I~8作用下衰变前后纠缠无变化,其他衰变纠缠度发生了变化;2)在其他的六个(I~±,U~±和V~±)超出李代数的生成元的作用下,三种混合介子态衰变前后组成成分发生了变化,其中两个衰变后变成单态,纠缠度为零;两个衰变不存在;剩余两个衰变后纠缠度发生了变化,此外在带电(K)和中性(K_I~0)两类K型混合介子态的六种可能的衰变中,两种类型的末态的纠缠度两两相同;3)三种混合介子态之间可以通过I~±,U~±和V~±算子循环转化,具有明显的对称性.本文从具有的对称性上提供了一种探索混合介子态可能衰变的方法,并且可以用此方法去预测可能的未知衰变粒子和解释己测得的衰变问题. 相似文献
6.
Michela Varagnolo 《Letters in Mathematical Physics》2000,53(4):273-283
We prove a conjecture of Nakajima (for type A it was announced by Ginzburg and Vasserot) giving a geometric realization, via quiver varieties, of the Yangian of type ADE (and more in general of the Yangian associated to every symmetric Kac–Moody Lie algebra). As a corollary, we get that the finite-dimensional representation theory of the quantized affine algebra and that of the Yangian coincide. 相似文献
7.
As the Yangian double with center, which is deformed from affine algebra by the additive loop parameter ?, we get the commutation relation and the bosonization of quantum ?-deformed Virasoro algebra. The corresponding Miura transformation, the associated screening operators and the BRST charge have been studied. Moreover, we also construct the bosonization for type Ⅰ and type Ⅱ intertwiner vertex operators. Finally, we show that the commutation relations of these vertex operators in the case of p′ = γ, p = γ - 1 and ? = π actually give the exact scattering matrix of the restricted sine-Gordon model. 相似文献
8.
We construct the transition operators in terms of the generators of the general Yangian and the reduced Yangian. By acting these operators on a two-qubit pure state, we find that the entanglement degrees of the states are all decreased from the certain values to zero for the reduced Yangian algebra, which makes the state disentangled. This result sheds new light on the physical meaning of Y (sl(2) ) in quantum information. 相似文献
9.
E. Ragoucy 《Czechoslovak Journal of Physics》2000,50(1):163-168
We present a self-contained formulation of the Nonlinear Schrödinger hierarchy and its Yangian symmetry in terms of deformed oscilator algebra (Z.F. algebra). The link between Yangian Y(gl
N) and finite W(gl
pN, N.gl
p) algebras is also illustrated in this framework. 相似文献
10.
《Nuclear Physics B》2005,717(3):361-386
We apply novel techniques in planar superconformal Yang–Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local Abelian Hamiltonians with periodic boundary conditions, and show that they annihilate the chiral primary states. We streamline the derivation of the R-matrix in a conventional spin model, and extend this computation to the gauge theory. We comment on higher-loop corrections and higher-loop integrability. 相似文献
11.
A new affine Hecke algebra is found in studying the XXZ model with a diagonal boundary condition. In the special case of T = 0, we give the double structure of this new affine Hecke algebra, which is similar to the Bn type affine Hecke algebra. 相似文献
12.
Letters in Mathematical Physics - We prove the equivalence of two presentations of the Yangian $$Y(\mathfrak {g})$$ of a simple Lie algebra $$\mathfrak {g}$$ , and we also show the equivalence with... 相似文献
13.
M. L. Nazarov 《Letters in Mathematical Physics》1991,21(2):123-131
We study a superanalogue of the Yangian of the Lie algebra gl
m
. We apply our constructions to invariant theory. 相似文献
14.
We show that a Yangian construction based on the algebra of an infinite number of harmonic oscillators (i.e. a vibrating string) terminates after one step, yielding the Virasoro algera. 相似文献
15.
T.T. Truong 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,5(3):697-703
We point out the existence of an alternative algebraic structure in Yang-Baxter algebra with trigonometric R-matrix, which appears to be the generalization of the Yangian in Yang-Baxter algebras with rational R-matrix and which is described most naturally by q-commutators. Some properties are presented, in particular in the case of the well-known symmetric six-vertex model.
Received: 13 February 1998 / Revised: 16 March 1998 / Accepted: 17 April 1998 相似文献
16.
《Nuclear Physics B》1999,561(3):385-412
Local conserved charges in principal chiral models in 1+1 dimensions are investigated. There is a classically conserved local charge for each totally symmetric invariant tensor of the underlying group. These local charges are shown to be in involution with the non-local Yangian charges. The Poisson bracket algebra of the local charges is then studied. For each classical algebra, an infinite set of local charges with spins equal to the exponents modulo the Coxeter number is constructed, and it is shown that these commute with one another. Brief comments are made on the evidence for, and implications of, survival of these charges in the quantum theory. 相似文献
17.
We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operaors for different energy levelsfor this system are obtained. 相似文献
18.
We construct a class of integrable generalization of Toda
mechanics with long-range interactions. These systems are
associated with the loop algebras L(Cr) and L(Dr) in the sense that their Lax matrices can be realized in
terms of the c=0 representations of the affine Lie algebras
C(1)r and
D(1)r and the interactions pattern involved
bears the typical characters of the corresponding root systems. We
present the equations of motion and the Hamiltonian structure.
These generalized systems can be identified unambiguously by
specifying the underlying loop algebra together with an ordered
pair of integers (n,m). It turns out that different systems
associated with the same underlying loop algebra but with
different pairs of integers
(n1,m1) and (n2,m2) with
n2<n1 and
m2<m1 can be related by a nested Hamiltonian
reduction procedure. For all nontrivial generalizations, the extra
coordinates besides the standard Toda variables are Poisson
non-commute, and when either $n$ or
m≥3, the Poisson
structure for the extra coordinate variables becomes some Lie
algebra (i.e. the extra variables appear linearly on the
right-hand side of the Poisson brackets). In the quantum case, such
generalizations will become systems with noncommutative variables
without spoiling the integrability. 相似文献
19.
We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operators for different energy levels for this system are obtained. 相似文献
20.
The spectral decomposition of the path space of the vertex model associated
to the vector representation of the quantized affine algebra
is studied. We give a one-to-one correspondence between
the spin configurations and the semistandard tableaux of skew Young diagrams.
As a result we obtain a formula of the characters for the degeneracy of the
spectrum in terms of skew Schur functions. We conjecture that our
result describes the -module contents
of the Yangian -module structures of the level 1 integrable modules of the affine Lie algebra .
An analogous result is obtained also for a vertex model
associated to the quantized twisted affine
algebra , where characters
appear for the degeneracy of the spectrum.
The relations to the spectrum of the Haldane-Shastry and
the Polychronakos
models are also discussed.
Received: 28 July 1996 / Accepted: 11 October 1996 相似文献