Differential Representations of SO（4） Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO（4）. These representations include the left and the right differential representations and the left and the right adjoint differential representations in both the group parameter space and its coset spaces. They are the generalization of the differential representations of the SO（3） rotation group in the Euler angles. These representations may find their applications in the study of the physical systems with SO（4） dynamical symmetry.     

Differential Representations of SO(4) Dynamical Group

In this paper we present systematic differential representations for the dynamical group SO(4). These representations include the left and the right differential representations and the left and the right adjoint differential representations in both the group parameter space and its coset spaces. They are the generalization of the differential representations of the SO(3) rotation group in the Euler angles. These representations may find their applications in the study of the physical systems with SO(4) dynamical symmetry.     

BRST cohomology and highest weight vectors. I

We initiate a program to study certain recent problems in non-compact coset CFT by the BRST approach. We derive a reduction formula for the BRST cohomology by making use of a twisting by highest weight modules. As illustrations, we apply the formula to the bosonic string model and a rank one non-compact coset model [DPL]. Our formula provides a completely new approach to non-compact coset construction.Partially supported by NSF Grant DMS-8703581     

Berezin quantization of gauged WZW and coset models

Gauged WZW and coset models are known to be useful to prove holomorphic factorization of the partition function of WZW and coset models. In this note we show that these gauged models can be also important to quantize the theory in the context of the Berezin formalism. For gauged coset models Berezin quantization procedure also admits a further holomorphic factorization in the complex structure of the moduli space.This work is dedicated to Professor Michel Ryan on the occasion of his 60th birthday.     

CONFINEMENT PROPERTIES OF PURE GAUGE FIELCS ON COSET SPACE OF THE NON-ABELIAN CHIRAL GROUP

In this paper the method of lattlce gauge theories is applied to the investigation of the effect of coset pure gauge fields of the non-Abelian chiral group on the confinement properties of a system. In particular, the current-current propagator of the coset G/H=SU(2)_L×(2)_r/SU(2) model is calculated. Then it IS found that the pure gauge fields-on coset space only offer a perimeter law factor which does not change the confinement properties of a physical system.     

LATTICE FORMULATION OF THE PURE GAUGE FIELDS ON COSET SPACE

In this paper we construct a lattice formulation of the pure gauge fields on a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a four-dimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the confinement properties of the quark system by calculating lattice current-current propagator when the coset pure gauge fields remain manifest.     

LATTICE FORMULATION OF THE PURE GAUGE FIELDS ON COSET SPACE

In this paper we construct the lattice formulation of the pure gauge fields in a coset space in the cases of a group G with non-trivial topological property and of a chiral group G, and present a local gauge invariant action of a quark system on a fourdimensional Euclidean space lattice, which has the continuum limit as usual. For non-chiral group with trivial topological property, it is shown that the coset pure gauge fields have no influence on the confinement properties of the quark system by calculating latt-ice current-current propagztor when the coset pure gauge fields are retained manifest1y.     

CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF AN ABELIAN CHIRAL GROUP

In this paper the lattice current-current propagator is calcdlated and the influence of coset pure gauge fields of an abelian chiral group G=U₁×U₁⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion in lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current current propagator which has no influence on confinement properties of the system. When subgroup H is U_s, the coset puregauge fields have no influence on wnfinement properties of the system either.     

BJORKEN-JOHNSON-LOW TECHNIQUE AND PERTURBATION STUDY ON CHIRAL ANOMALY IN ABELIAN COSET PURE GAUGE FIELD THEORY

The perturbation theory in coset pure gauge field theory is studied for the first time in this paper.By using the Bjorken-Johnson-Low technique and calculating the Schwinger term in related commutators,the anomalous Ward identity in Abelian coset pure gauge field theory is derived,which is consistent with the non-perturbative calculation.     

Unitary construction of extended conformal algebras

Particular examples and the general structure of extended conformal symmetries in coset conformal field theories are discussed. Discrete series of unitary representations, whose existence had been previously conjectured, are constructed for a class of extended conformal algebras introduced by Fateev and Zamolodchikov (FZ). The construction is a generalisation of the coset construction of the discrete series for the superconformal algebra using the coset spaces so(N) ⊕ su(N)/so(N), for fixed N. The N = 3 series is the FZ S₃ algebra and the N = 4 series consists of two commuting copies of the superconformal algebra. A general method for analysing the extended conformal symmetries present in a particular coset theory and of constructing discrete series of representations of extended symmetry algebras is outlined.     

Compactification over coset spaces with torsion and vanishing cosmological constant

We consider the compactification of ten-dimensional Einstein-Yang-Mills theories over non-symmetric, six-dimensional homogeneous coset spaces with torsion. We examine the Einstein-Yang-Mills equations of motion requiring vanishing cosmological constant at ten and four dimensions and we present examples of compactictifying solutions. It appears that the introduction of more than one radii in the coset space, when possible, may be mandatory for the existence of compactifying solutions.     

CONFINEMENT PROPERTIES OF THE PURE GAUGE FIELDS ON COSET SPACE OF AN ABELIAN CHIRAL GROUP

In this paper the lattice current-current propagator is calculated and the influence of coset pure gauge fields of an Abelian chiral group G=U₁×U⁵ on confinement properties of a quark system is discussed by virtue of the Wilson's criterion of lattice gauge theory. When subgroup H is U₁, the coset pure gauge fields only contribute a perimeter law factor to the current-current propagator which has no influence on confinement properties of the system. When subgroup H is U⁵, the coset pure gauge fields also have no influence on confinement properties of the system.     

分子高激发振动态的动力学特性研究

运用经典哈密顿代数方法,结合单摆的运动特点表示两个化学键之间的振动耦合.对水分子高激发态下两个氧氢键(O—H)伸缩振动动力学的研究结果表明,靠近分界线的中间能级的相空间中较易出现混沌轨道,而较高或较低能级的相空间中则具有比较规则的周期运动 关键词： 高激发振动 共振 混沌     

A result on certain coset subalgebras of the βγ-system

In this paper, for the highest weight module V4 of sl(2,C) with the highest weight 4, we describe subalgebras Sβ(V4)θ+ and Sγ(V4)θ+ of the βγ-system coset S(V4)θ+ by giving their generators. These coset subalgebras are interesting, new examples of strongly finitely generated vertex algebra.     

Factored coset models: a unifying approach to different bosonization schemes

We discuss various bosonization schemes from a path integral perspective. Our analysis shows that the existence of different bosonization schemes, such as abelian bosonization of non-abelian models and non-abelian bosonization of fermions with colour and flavour indices, can be understood as different ways of factoring out a dynamically trivial coset which contains the fermions. From this perspective follows the importance of the coset model in ensuring the correct superselection rules on the bosonic level.     

Topological Conformal Field Theories from the Noncompact Coset Models

It is shown in this letter that in the bosonic coset models G_kl×G_k2/G_kl+_k2 associated with noncompact Kac-Moody algebra there exist two kinds of topological points, _k2=0 and _kl+_k2-2g = 0. At these points, the coset models may be interpreted as twisted versions of noncompact counterparts of the Kazama-Suzuki models.     

G/H conformal field theory from gauged WZW model

We show that the coset construction for affine algebras ĝ ⊃ ĥ can be realized by coupling a group G WZW model to a gauge field taking values in the Lie algebra h. The partition function of the coset models is computed exactly in terms of the branching functions of ĝ⊃ĥ. Correlation functions may be expressed in terms of those of the G-valued WZW model and of the H_scc/H-valued one, also exactly soluble. The special cases include unitary, superconformal, paramefermionic and other discrete series.     

Algebraic Coset Conformal Field Theories

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess–Zumino–Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and ideas of algebraic quantum field theory to approach coset Conformal Field Theories. Two conjectures are formulated and their consequences are discussed. Some results are presented which prove the conjectures in special cases. In particular, one of the results states that a class of representations of coset W _N (N≥ 3) algebras with critical parameters are irreducible, and under the natural compositions (Connes' fusion), they generate a finite dimensional fusion ring whose structure constants are completely determined, thus proving a long-standing conjecture about the representations of these algebras. Received: 5 November 1998 / Accepted: 18 October 1999     

Performance of lattice coset codes on Universal Software Radio Peripherals

We consider an experimental setup of three Universal Software Radio Peripherals (USRPs) that implement a wiretap channel, two USRPs are the legitimate players Alice and Bob, while the third USRP is the eavesdropper, whose position we vary to evaluate information leakage. The experimented channels are close to slow fading channels, and coset coding of lattice constellations is used for transmission, allowing to introduce controlled randomness at the transmitter. Simulation and measurement results show to which extent coset coding can provide confidentiality, as a function of Eve’s position, and the amount of randomness used.     

Yangian symmetry in integrable quantum gravity

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.