共查询到20条相似文献,搜索用时 31 毫秒
1.
CP 《Journal of Geometry and Physics》1998,28(3-4):384-406
It is known that symmetric orbits in g* for any simple Lie algebra g are equipped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the “canonical” R-matrix. We realize quantization of the Poisson pencil CPn type orbits (i.e. orbits in sl(n + 1)* whose real compact form is CPn) by means of q-deformed Verma modules. 相似文献
2.
We state and prove the theorem of existence and uniqueness of solutions to ordinary superdifferential equations on supermanifolds. It is shown that any supervector field, X = X0 + X1, has a unique integral flow, Г:
1¦1 x (M, AM) → (M, AM), satisfying a given initial condition. A necessary and sufficient condition for this integral flow to yield an
1¦1-action is obtained: the homogeneous components, X0, and, X1, of the given field must define a Lie superalgebra of dimension (1, 1). The supergroup structure on
1¦1, however, has to be specified: there are three non-isomorphic Lie supergroup structures on
1¦1, all of which have addition as the group operation in the underlying Lie group
. On the other extreme, even if X0, and X1 do not close to form a Lie superalgebra, the integral flow of X is uniquely determined and is independent of the Lie supergroup structure imposed on
1¦1. This fact makes it possible to establish an unambiguous relationship between the algebraic Lie derivative of supergeometric objects (e.g., superforms), and its geometrical definition in terms of integral flows. It is shown by means of examples that if a supergroup structure in
1¦1 is fixed, some flows obtained from left-invariant supervector fields on Lie supergroups may fail to define an
1¦1-action of the chosen structure. Finally, necessary and sufficient conditions for the integral flows of two supervector fields to commute are given. 相似文献
3.
Frank Antonsen 《International Journal of Theoretical Physics》1998,37(2):697-757
We first introduce theWigner–Weyl–Moyal formalism for a theorywhose phase space is an arbitrary Lie algebra. We alsogeneralize to quantum Lie algebras and to supersymmetrictheories. It turns out that the noncommutativity leads to a deformation ofthe classical phase space: instead of being a vectorspace, it becomes a manifold, the topology of which isgiven by the commutator relations. It is shown in fact that the classical phase space, for asemisimple Lie algebra, becomes a homogeneous symplecticmanifold. The symplectic product is also deformed. Wefinally make some comments on how to generalise to C*-algebras and other operator algebras,too. 相似文献
4.
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
5.
André Lichnerowicz 《Letters in Mathematical Physics》1979,3(6):495-502
The twisted products play an important role in Quantum Mechanics [1, 2]. We introduce here a distinction between Vey *ν-products and strong Vey *ν-products and prove that each *ν-product is equivalent to a Vey *ν-product. If b
3(W)=0, the symplectic manifold (W, F) admits strong Vey *ν-products. If b
2(W)=0, all *ν-products are equivalent as well as the Vey Lie algebras. In the general case, we characterize the formal Lie algebras which
are generated by a *ν-product and we prove that the existence of a *ν-product is equivalent to the existence of a formal Lie algebra infinitesimally equivalent to a Vey Lie algebra at the first
order. 相似文献
6.
7.
Yuching You 《Physica D: Nonlinear Phenomena》1991,50(3):429-462
In a series of papers, Date, Jimbo, Kashiwara and Miwa (DJKM) studied soliton equations using representation of Lie algebras. In particular, they found a remarkable new hierarchy of KP type, namely BKP. One can also study the same problem using vertex operators for the infinite rank affine Lie algebras
∞,
∞. Combining the ideas of Kac and DJKM, we found the realization of the basic representation and the half spin representations for
∞ as well. In particular, we show that DKP and BKP are essentially the same, moreover, one gets a modified DKP hierarchy. 相似文献
8.
We present an axiomatic formulation of a new class of infinitedimensional Lie algebras-the generalizations ofZ-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras continuum Lie algebras. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. 相似文献
9.
We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra \bar{E} of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson (GJ) hierarchy whose Hamiltonian structure can
also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra \tilde{E} of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell (KN) hierarchy which, consisting of two arbitrary parametersα andβ, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra \tilde{F} of the Lie algebra F to obtain an
expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations. 相似文献
10.
We intend to realize the step-up and step-down operators of the potential V (x) = V1 e 2βx + V2 e βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β → -β). 相似文献
11.
Paolo Casati Gregorio Falqui Franco Magri Marco Pedroni 《Journal of Geometry and Physics》1998,26(3-4):291-310
We discuss the geometry of the Marsden-Ratiu (MR) reduction theorem for a bihamiltonian manifold. We consider the case of the manifolds associated with the Gel'fand-Dickey theory, i.e., loop algebras over. We provide an explicit identification, tailored on the MR reduction, of the Adler-Gel'fand-Dickey brackets (AGD) with the Poisson brackets on the reduced bihamiltonian manifold
. Such an identification relies on a suitable immersion of T*N into the algebra of pseudodifferential operators connected to geometrical features of the theory of (classical)
n-algebras. 相似文献
12.
In this paper we study the finitely generated algebras underlyingW algebras. These so called finiteW algebras are constructed as Poisson reductions of Kirillov Poisson structures on simple Lie algebras. The inequivalent reductions are labeled by the inequivalent embeddings ofsl
2 into the simple Lie algebra in question. For arbitrary embeddings a coordinate free formula for the reduced Poisson structure is derived. We also prove that any finiteW algebra can be embedded into the Kirillov Poisson algebra of a (semi)simple Lie algebra (generalized Miura map). Furthermore it is shown that generalized finite Toda systems are reductions of a system describing a free particle moving on a group manifold and that they have finiteW symmetry. In the second part we BRST quantize the finiteW algebras. The BRST cohomology is calculated using a spectral sequence (which is different from the one used by Feigin and Frenkel). This allows us to quantize all finiteW algebras in one stroke. Examples are given. In the last part of the paper we study the representation theory of finiteW algebras. It is shown, using a quantum version of the generalized Miura transformation, that the representations of finiteW algebras can be constructed from the representations of a certain Lie subalgebra of the original simple Lie algebra. As a byproduct of this we are able to construct the Fock realizations of arbitrary finiteW algebras. 相似文献
13.
ZHANG Yu-Feng DONG Huang-He Honwah Tam 《理论物理通讯》2007,48(2):215-226
Starting from the subgroups of the group U(n), the corresponding Lie algebras of the Lie algebra Al are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given. 相似文献
14.
The dynamical cluster-decay model (DCM) is employed to investigate the decay of 68,70Ge* compound nuclei formed respectively via tightly (4He) and loosely (6He) bound projectiles, using 64Zn target. The study is carried out over a wide energy range (Ec.m.~5 MeV to 16 MeV) by including the quadrupole deformations (β2i) and optimum orientations (θiopt) of the decaying fragments. The fusion cross-sections, obtained by adding various evaporation channels show nice agreement with the experimental data for 4He+64Zn reaction. The contribution from competing compound inelastic scattering channel is also analyzed particularly for 68Ge* nucleus at above barrier energies. On the other hand, the decrement in the fusion cross-sections of 70Ge* nuclear system is addressed by presuming that 65Zn ER is formed via two different modes:(i) the αn evaporation of 70Ge* nucleus, and (ii) 1n-evaporation of 66Zn* nuclear system, formed via breakup and 2n-transfer channels due to halo structure of the 6He projectile. Besides this, the suppression in 2np evaporation cross-sections suggests the contribution of another breakup and transfer process of 6He i.e. 4He+64Zn. The contribution of breakup+transfer channels for 6He+64Zn reaction is duly addressed by applying relevant energy corrections due to the breakup of " 6He" projectile into 2n and 4He. In addition to this, the barrier lowering, angular momentum and energy dependence effects are also explored in view of the dynamics of chosen reactions. 相似文献
15.
P. Lecomte 《Letters in Mathematical Physics》1979,3(5):405-411
This letter presents a study of the automorphisms and the derivations of a large class of local Lie algebras over a manifold M (in the sense of Shiga and Kirillov) called Lie algebras of order O over M.It is shown that, in general, the algebraic structure of such an algebra characterizes the differentiable structure of M and that the Lie algebra of derivations of is a Lie algebra of differential operators of order 1 over M obtained in a natural way as the space of sections of a vector bundle canonically associated to . 相似文献
16.
By deforming the symplectic structure on S2, we get the q-deformation of SU(2) algebra at classical level, SUq,h→0(2), in a Hamiltonian approach. Furthermore, we construct a set of operators on the line bundle over the deformed symplectic manifo1d.Sq2 such that they form SUq,h→0(2) in Lie brackets and set up a nontrivial Hopf algebra with a parameter q only in such a classical Hamiltonian system. We also show that the deformations from Sq2 to Sq2 are a set of quasiconformal transformations. The quantization via geometric approach of the system gives rise to the quantum q-deformed algebra SUq,h(2), wnich has a Hopf algebraic structure with two independent parameters q and h. 相似文献
17.
K. D. Kirchberg 《Journal of Geometry and Physics》1990,7(4):449-468
If M2m is a closed Kähler spin manifold of positive scalar curvature R, then each eigenvalue λ of type r (r {1, …, [(m + 1)/2]}) of the Dirac operator D satisfies the inequality λ2 ≥ rR0/4r − 2, where R0 is the minimum of R on M2m. Hence, if the complex dimension m is odd (even) we have the estimation for the first eigenvalue of D. In the paper is also considered the limiting case of the given inequalities. In the limiting case with m = 2r − 1 the manifold M2m must be Einstein. The manifolds S2, S2 × S2, S2 × T2, P3(
), F(
), P3(
) × T2 and F(
3) × T2, where F(
3) denotes the flag manifold and T2 the 2-dimensional flat torus, are examples for which the first eigenvalue of the Dirac operator realizes the limiting case of the corresponding inequality. In general, if M2m is an example of odd complex dimension m, then M2m × T2 is an example of even complex dimension m + 1. The limiting case is characterized by the fact that here appear eigenspinors of D2 which are Kählerian twistor-spinors. 相似文献
18.
By using a six-dimensional matrix Lie algebra [Y.F. Zhang and Y. Wang, Phys. Lett. A 360 (2006) 92],
three induced Lie algebras are constructed. One of them is obtained by extending Lie bracket, the others are
higher-dimensional complex Lie algebras constructed by using linear transformations. The equivalent Lie algebras of the later two with multi-component forms are obtained as well. As their applications, we derive an integrable coupling and
quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations. 相似文献
19.
By making use of the vector product in R3, a commuting operation is introduced so that R3 becomes a Lie algebra. The resulting loop algebra \tilde R3 is presented, from which the well-known AKNS hierarchy is produced. Again via applying the superposition of the commuting operations of the Lie algebra, a commuting operation in
R6 is constructed so that
R6 becomes a Lie algebra. Thanks to the corresponding loop algebra \tilde R3 of the Lie algebra R3, the integrable coupling of the AKNS
system is obtained. The method presented in this paper is rather
simple and can be used to work out integrable coupling systems of
the other known integrable hierarchies of soliton equations. 相似文献
20.
The elliptic Calogero-Moser Hamiltonian and Lax pair associated with a general simple Lie algebra G are shown to scale to the (affine) Toda Hamiltonian and Lax pair. The limit consists in taking the elliptic modulus τ and the Calogero-Moser couplings m to infinity, while keeping fixed the combination M = m eiδθτ for some exponent δ. Critical scaling limits arise when 1/δ equals the Coxeter number or the dual Coxeter number for the untwisted and twisted Calogero-Moser systems respectively; the limit consists then of the Toda system for the affine Lie algebras G(1) and (G(1))V. The limits of the untwisted or twisted Calogero-Moser system, for δ less than these critical values, but non-zero, consists of the ordinary Toda system, while for δ = 0, it consists of the trigonometric Calogero-Moser systems for the algebras G and GV respectively. 相似文献