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1.
For an N-body Stark Hamiltonian , the resolvent estimate holds uniformly in with Re and Im , where , and is a compact interval. This estimate is well known as the limiting absorption principle. In this paper, we report that by introducing the localization in the configuration space, a refined resolvent estimate holds uniformly in with Re and Im . Dedicated to Professor Hideo Tamura on the occasion of his 60th birthday  相似文献   

2.
A family of polynomial -functions for the NLS-Toda hierarchy is constructed. The hierarchy is associated with the homogeneous vertex operator representation of the affine algebra of type A 1 (1). These -functions are given explicitly in terms of Schur functions that correspond to rectangular Young diagrams. It is shown that an arbitrary polynomial -function which is an eigenvector of d, the degree operator of , is contained in the family. By the construction, any -function in the family becomes a Virasoro singular vector. This consideration gives rise to a simple proof of known results on the Fock representation of the Virasoro algebra with c = 1.  相似文献   

3.
We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 107 producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).  相似文献   

4.
A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.   相似文献   

5.
The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential . A thermodynamic limit of quantum Gibbs state, a *-algebra and an automorphism group t for which is a KMS state are constructed.  相似文献   

6.
It was shown in an earlier paper that there is an Abelian extension of the general linear algebra gl 2, that contains the current algebra with anomaly in 3+1 dimensions. We construct a three-parameter family of deformations of . For certain choices of the deformation parameters, we can construct unitary representations. We also construct highest-weight nonunitary representations for all choices of the parameters.This work was supported in part by U.S. Department of Energy Contract No. DE-AC02-76ER13065.  相似文献   

7.
The universal R-matrix for a class of esoteric (nonstandard) quantum groups q(gl(2N+1)) is constructed as a twisting of the universal R-matrix S of the Drinfeld–Nimbo quantum algebras. The main part of the twisting cocycle is chosen to be the canonical element of an appropriate pair of separated Hopf subalgebras (quantized Borel's (N) q (gl(2N+1))), providing the factorization property of . As a result, the esoteric quantum group generators can be expressed in terms of Drinfeld and Jimbo.  相似文献   

8.
We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c 1,c 2 suchthat the corresponding eigenvalue satisfies for all sufficiently small.  相似文献   

9.
The paramagnetic state (+e) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: Si = 1.45(3) s, Te = 12.5(8) s at 290 K, Te = 12(2) s at 250 K.  相似文献   

10.
Let be an invariant state of theC*-system { ,G, } on a locally compact noncommutative groupG. Assume further that is extremal -invariant for an action of an amenable groupH which is -asymptotically abelian and commutes with . Denoting byF AB,G AB the corresponding two point functions, we give criteria for the fulfillment of the KMS condition with respect to some one parameter subgroup of the center ofG based on the existence of a closable mapT such thatTF AB=G AB for allA,B . Closability is either inL (G),B(G) orC (G), according to clustering properties for . The basic mathematical technique is the duality theory for noncompact, noncommutative locally compact groups.This work is supported in part by the National Science Foundation, Grant MCS 79-03041  相似文献   

11.
Given n2, we put r=min . Let be a compact, C r -smooth surface in n which contains the origin. Let further be a family of measurable subsets of such that as . We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator in L 2( n ), where is a positive constant, as . An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve.  相似文献   

12.
The electronic absorption coefficient (e) of meso-ultrasound (p –1 en, t, ee; ql 1, where p, en, t are the times of pulse relaxation, energy, and current carrier traps; ee –1 is the frequency of intraelectron collisions; , q are the frequency and wave vector of sound; l is the carrier mean free path) in the presence of a permanent external field E0 e 0 –1 q0T is calculated for anisotropic single-valley semiconductors with piezoelectrical and potential-deformation acoustoelectronic interaction. Considered arbitrary are: 1) the anisotropy of the tensors * and p (and other crystal parameters); 2) the degree of Fermi degeneration of the carriers; 3) the dependence of p on the carrier energy . The acoustoheat nonlinearity is neglected. The possibility of meso-ultrasound amplification by the transverse field (E0 - q) is predicted. By changing the orientation of the vector q relative to the crystal axes, the transverse threshold field (E thr ) can be controlled smoothly and within broad limits, This permits the production of a mechanical sound-amplification regulator or a modulator of its intensity. The ratio between E thr and E thr yields a measure of the relative anisotropy of the mobility.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 87–92, February, 1977.  相似文献   

13.
We consider Kontsevich star products on the duals of Lie algebras. Such a star product is relative if, for any Lie algebra, its restriction to invariant polynomial functions is the usual pointwise product. Let be a fixed Lie algebra. We shall say that a Kontsevich star product is -relative if, on *, its restriction to invariant polynomial functions is the usual pointwise product. We prove that, if is a semi-simple Lie algebra, the only strict Kontsevich -relative star products are the relative (for every Lie algebras) Kontsevich star products.  相似文献   

14.
Given a simple, simply laced, complex Lie algebra corresponding to the Lie group G, let be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra whose underlying graded commutative algebra is given by the cohomology, with respect to , of the algebra of regular functions on G with values in . We conjecture that describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical string. The conjecture is verified in the two explicitly known cases, 2 (the Virasoro string) and 3 (the string).  相似文献   

15.
We show that the affine quantum group is isomorphic to a bicross-product central extension of the quantum loop group by a quantum cocycle in R-matrix form.  相似文献   

16.
The two-dimensional massive Thirring model is described as the integrability condition of a pair of commuting completely integrable isospectral Hamiltonian flows in the dual (2)+* of the positive part (2)+ of the twisted loop algebra (2). Action-angle coordinates corresponding to the spectral invariants are derived on rational coadjoint orbits and a linearization of the flows obtained in the Jacobi variety of the underlying invariant spectral curve through a Liouville generating function for canonical coordinates.Research supported in part by the Natural Sciences Engineering Research Council of Canada and the Fonds FCAR du Québec.  相似文献   

17.
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.  相似文献   

18.
The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group in the following manner. There is a partition into disjoint subsets and a bijection between and the sectors of the (p,q)-minimal model such that the fusion rules correspond to where .  相似文献   

19.
20.
We give a complete characterization, including a Lévy–Itô decomposition, of Poincaré-invariant Markov processes on , the relativistic phase space in 1+1 spacetime dimensions. Then, by means of such processes, we construct Poincaré-invariant Gaussian random fields, and we prove a no-go theorem for the random fields corresponding to Brownian motions on .  相似文献   

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