Continued fraction representation of correlation functions

A continued fraction representation of the Laplace transform of time correlation functions is obtained for a class of dynamical systems. The connection with the work of Mori is discussed.     

Free boson representation ofU_q (\widehat{sl}_3 )

A representation of the quantum affine algebra of an arbitrary levelk is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in theq 1 limit. The analogues of the screening currents are also obtained. They commute with the action of modulo total differences of some fields.On leave from Department of Physics, University of Tokyo, Tokyo 113, Japan.     

The poisson representation. II Two-time correlation functions

Basic formulas for the two-time correlation functions are derived using the Poisson representation method. The formulas for the chemical system in thermodynamic equilibrium are shown to relate directly to the fluctuationdissipation theorems, which may be derived from equilibrium statistical mechanical considerations. For nonequilibrium systems, the formulas are shown to be generalizations of these fluctuation-dissipation theorems, but containing an extra term which arises entirely from the nonequilibrium nature of the system. These formulas are applied to two representative examples of equilibrium reactions (without spatial diffusion) and to a nonequilibrium chemical reaction model (including the process of spatial diffusion) for which the first two terms in a systematic expansion for the two-time correlation functions are calculated. The relation between the Poisson representation method and Glauber-SudarshanP-representation used in quantum optics is discussed.     

Spectra,eigenvectors and overlap functions for representation operators ofq-deformed algebras

Operators of representations corresponding to symmetric elements of theq-deformed algebrasU _q (su_1,1),U _q (so_2,1),U _q (so_3,1),U _q (so _n ) and representable by Jacobi matrices are studied. Closures of unbounded symmetric operators of representations of the algebrasU _q (su_1,1) andU _q (so_2,1) are not selfadjoint operators. For representations of the discrete series their deficiency indices are (1,1). Bounded symmetric operators of these representations are trace class operators or have continuous simple spectra. Eigenvectors of some operators of representations are evaluated explicitly. Coefficients of transition to eigenvectors (overlap coefficients) are given in terms ofq-orthogonal polynomials. It is shown how results on eigenvectors and overlap coefficients can be used for obtaining new results in representation theory ofq-deformed algebras.     

Free boson realization of

We construct a realization of the quantum affine algebra of an arbitrary level k in terms of free boson fields. In the q1 limit this realization becomes the Wakimoto realization of. The screening currents and the vertex operators (primary fields) are also constructed; the former commutes with modulo total difference, and the latter creates the highest weight state from the vacuum state of the boson Fock space.fellow of Soryushi ShogakukaiAddress after June 1: Department of Physics, Faculty of Liberal Arts, Shinshu University, Matsumoto 390, Japan     

Semiclassical correlation functions of Wilson loops and local vertex operators

We analyze correlation functions of Wilson loop observables and local vertex operators within the strong-coupling regime of the AdS/CFT correspondence. When the local operator corresponds to a light string state with finite conserved charges the correlation function can be evaluated in the semiclassical approximation of large string tension, where the contribution from the light vertex can be neglected. We consider the cases where the Wilson loops are described by two concentric surfaces and the local vertices are the superconformal chiral primary scalar or a singlet massive scalar operator.     

The unitary representation operators

A representation (called theU-representation) which remains unitary for all spins and for all ranges of velocities was obtained by us in a recent paper. We obtain here relevant expressions for the boosts operator and the observables in such a representation.     

Dobiński relations and ordering of boson operators

We introduce a generalization of the Dobiński relation, through which we define a family of Bell-type numbers and polynomials. Such generalized Dobiński relations are coherent state matrix elements of expressions involving boson ladder operators. This may be used in order to obtain normally ordered forms of polynomials in creation and annihilation operators, both if the latter satisfy canonical and deformed commutation relations.     

On the normal ordering of multi-mode boson operators

Combinatorial aspects of normal ordering for annihilation and creation operators of a multi-mode boson system are discussed. The modes are assumed to be coupled, since otherwise the problem of normal ordering is reduced to the cooresponding problem of the single-mode case. To describe the normal ordering in the multi-mode case, for each mode, a color is introduced, and colored contractions are considered. A depiction for colored contractions via colored linear representations is given. By analogy with the single-mode case, associated colored Stirling numbers are defined as coefficients appearing in the process of normal ordering for powers of the number operators. Several properties of these colored Stirling numbers are discussed.     

Effective dielectric functions of alkali halide composites and their spectral representation

In the electrostatic approximation inhomogeneous samples with characteristic scale of inhomogeneities much smaller than the wavelength of light can be characterized by an effective dielectric function _eff. This paper analyzes in which cases simple mixing formulas can be used to calculate _eff from the dielectric functions of the consituents. These considerations are compared with reflectance measurements of alkali halide composites in the far infrared. In many cases it turns out that it is essential to employ the general ansatz of the Bergman spectral representation in order to describe all effects due to the geometrical arrangement of the phases in a proper manner. It is necessary to adjust Bergman's spectral density to measurements. This can be done by use of a Monte-Carlolike algorithm. Further on we try to answer the question how to extract the dielectric function of one of the constituents from measurements of the effective dielectric function.     

Free field construction for correlation functions of the eight-vertex model

A free field representation for the type I vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to express correlation functions of the eight-vertex model in terms of correlation functions of the SOS model with a non-local insertion. This new non-local insertion admits a free field representation in terms of Lukyanov's screening operator. The spectrum of the corner transfer matrix and the Baxter-Kelland formula for the average staggered polarization have been reproduced.     

Formal power series representation for gauge boson stars

We represent spherically symmetric, static, and non-singular solutions of the Einstein SU(2)-Yang-Mills and the Yang-Mills-dilaton system by means of formal power series expansions. Their coefficients are algebraically expressed in terms of new recursion relations. The solutions of Bartnik and McKinnon, found by numerical integration, are contained in our solution manifold.     

On the correspondence between fermion and boson states and operators

Mapping of shell-model (fermion) Hamiltonians onto boson Hamiltonians which underly the interaction boson model ^1–5) is investigated. A simple correspondence is defined and a sufficient condition given for shell-model Hamiltonians to simply correspond to finite hermitian boson Hamiltonians. A special case is discussed where diagonalization of a shell-model Hamiltonian for valence protons and neutrons can be exactly carried out in an equivalent (but different) boson space. If, however, the proton Hamiltonian and neutron Hamiltonian are diagonal in the seniority scheme, mapping of fermion states onto orthogonal boson states cannot be a simple correspondence. In that case the boson quadrupole operators equivalent to fermion guadrupole operators cannot be single-boson operators but must be more complicated, ones.     

非线性两模玻色子系统的Majorana表象

利用Majorana表象,从平均场模型和二次量子化模型两方面研究了非线性双模玻色子系统的动力学问题.得到了Majorana点在球面上的运动方程,分析了平均场模型和二次量子化模型之间的区别及其在Majorana点运动方程中的体现.研究了二次量子化模型中量子态在少体和多体情况下的动力学演化及其与平均场量子态的区别和联系.以平均场模型和二次量子化模型量子态之间的保真度和Majorana点之间的关联为手段,讨论了在不同玻色子间相互作用强度、不同玻色子数下量子态的演化及相应的自囚禁效应.     

Normal and antinormal ordering of boson operator functions

It is shown that the divergences associated with antinormally ordered forms of boson operators, as discovered computationally by Baltin, is due to an unjustifiable interchange of order of summation.     

Dyson boson mapping theory including ground-state correlation

Since the usual boson mapping methods are based on either Tamm-Dancoff phonons or bare fermion pairs, the ground-state correlation is not well taken into account by them. To improve this, we propose a new treatment of Dyson boson mapping based on a modification of the RPA phonon, which is used in the practical treatment of the self-consistent collective-coordinate (SCC) method. Applying this new method to a solvable SU(3) model and comparing the results with the exact solutions, we show that it is a good improvement of the usual Dyson boson mapping method. We also compare this method with the quantized first-order Dyson-type representation of the SCC method, which can be considered as another way to include the ground-state correlation in a boson mapping.     

Recast combination functions of coordinate and momentum operators into their ordered product forms

By using the parameter differential method of operators, we recast the combination function of coordinate and momentum operators into its normal and anti-normal orderings, which is more ecumenical, simpler, and neater than the existing ways. These products are very useful in obtaining some new differential relations and useful mathematical integral formulas. Further, we derive the normally ordered form of the operator(fQ+gP)~(-n) with n being an arbitrary positive integer by using the parameter tracing method of operators together with the intermediate coordinate–momentum representation. In addition, general mutual transformation rules of the normal and anti-normal orderings, which have good universality, are derived and hence the anti-normal ordering of( fQ + gP)~(-n) is also obtained. Finally, the application of some new identities is given.     

Determinant representation for correlation functions of spin-1/2 XXX and XXZ Heisenberg magnets

We consider zero temperature correlation functions of the spin-1/2 XXZ Heisenberg chain in the critical regime –1<1 in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in term of determinats of Fredholm integral operators.