General relations among observables in a large class of neutral-current processes mediated by one,two, or threeZ bosons

Without assuming any symmetry amongμ, e andτ leptons, we consider several neutral current processes involving 73 physical parameters and deduce general relations among them implied by different classes of gauge models with one, two and three neutralZ bosons. In the single-Z boson model there are 60 general relations while the two (three)-boson model leads to 48 (36) relations. If onlyμ-e universality is imposed, the physical parameters reduce to 41 and the single (two)-Z boson model yields 31 (22) relations, while only 13 relations exist for the threeZ boson model. Imposingμ-e-τ universality decreases the number of physical parameters to 18, while the number of relations in the single- and two-Z boson models reduces to 11 and 5, respectively. In these relations are contained those obtained by Hung and Sakurai and Parida and Rajasekaran in the corresponding cases. In addition we obtain some new inequalities among the observable parameters which are to be satisfied by all gauge models.     

Partial Wave Crossing Relations for Meson-Baryon Scattering

Three different types of relations for meson-baryon partial wave amplitudes following from the s ↔ u crossing symmetry of the invariant amplitudes are investigated: i) the partial wave crossing relations directly derived from the s ↔ u crossing symmetry and the partial wave projection, ii) the partial wave crossing relations following from a combined use of s ↔ u crossing symmetry and analyticity, and iii) the crossing sum rules, which are a direct consequence of the s ↔ u crossing symmetry. The kernels entering the crossing relations i) and ii) are given in an analytic form, valid for arbitrary angular momentum. Their properties are studied in detail. By means of the partial wave crossing relations ii) it is demonstrated that u-channel exchange of a resonance leads to a resonance-like behaviour of the partial wave amplitudes on the crossed physical cut. This phenomenon is described in terms of “pseudoresonances”. Finally the crossing sum rules iii) and their practical use are thoroughly discussed, and they are compared with the partial wave crossing relations i) and ii). Special attention is paid to the crossing symmetry constraints on the S-wave amplitudes. As a result of these investigations we present a crossing symmetric ansatz for these amplitudes which gives a more reliable parametrization than the usual effective range approximation.     

πN Partial Wave Relations from Fixed-t Dispersion Relations

Starting from fixed-t dispersion relations we derive a set of relations for the πN partial wave amplitudes, generalizing previous work of OEHME [1], CAPPS and TAKEDA [2], and CHEW , GOLDBERGER , LOW and NAMBU [3]. Our relations contain a single integral kernel, which is agiven in a closed form valid for arbitrary angular momentum. This kernel correlates the imaginary parts of all partial wave amplitudes with the partial wave amplitude under consideration. The partial wave relations give the correct threshold behaviour. The region of convergence is determined in the case of axiomatic field theory and in the case of Mandelstam analyticity. Possible applications are discussed.     

General relations among observables in neutral-current phenomena mediated by one or twoZ bosons

Ifμ-e universality is assumed, there are 17 neutral-current parameters of current experimental interest, including the parity-violating nuclear force sector. We deduce the general relations among these parameters implied by gauge models. In single-Z boson models, there are 10 relations, while two-boson models lead to 4 relations. Ifμ-e universality is abandoned, the number of parameters increases to 31, while the number of relations becomes 21 in single-boson models and 12 in two-boson models. We derive all these relations.     

Recursion Relations for Unitary Integrals,Combinatorics and the Toeplitz Lattice

 In a discussion in spring 2001, Alexei Borodin showed us recursion relations for the Toeplitz determinants going with the symbols e ^{t(z + z−1)} and \!. Borodin obtained these relations using Riemann-Hilbert methods; see the recent work of Borodin B and Baik Baik. The nature of Borodin's recursion relations pointed towards the Toeplitz lattice and its Virasoro algebra, introduced by us in AvM1. In this paper, we take the Toeplitz lattice and Virasoro algebra approach for a fairly large class of symbols, leading to a systematic way of generating recursion relations. The latter are very naturally expressed in terms of the L-matrices appearing in the Toeplitz lattice equations. As a surprise, we find, compared to Borodin's, a different set of relations, except for the 3-step relations associated with the symbol e ^{t(z + z−1)} . The Painlevé analysis of the Toeplitz lattice enables us to show the ``singularity confinement' for these recursion relations. Received: 30 January 2002 / Accepted: 6 January 2003 Published online: 19 May 2003 RID="⋆" ID="⋆" The support of a National Science Foundation grant DMS-01-00782 is gratefully acknowledged. RID="⋆⋆" ID="⋆⋆" The support of a National Science Foundation grant DMS-01-00782, a Nato, a FNRS and a Francqui Foundation grant is gratefully acknowledged. Communicated by L. Takhtajan     

sl(N) Onsager's algebra and integrability

We define ansl(N) analog of Onsager's algebra through a finite set of relations that generalize the Dolan-Grady defining relations for the original Onsager's algebra. This infinite-dimensional Lie algebra is shown to be isomorphic to a fixed-point subalgebra ofsl(N) loop algebra with respect to a certain involution. As the consequence of the generalized Dolan-Grady relations a Hamiltonian linear in the generators ofsl(N) Onsager's algebra is shown to posses an infinite number of mutually commuting integrals of motion.     

On the defining relations of quantum superalgebras

In defining quantum superalgebras, extra relations need to be added to the Serre-like relations. They are obtained for sl _q (m, n) and osp _q (m, 2n) usingq-oscillator representations.Supported in part by the National Sciences and Engineering Research Council (NSERC) of Canada.     

Deformations of enveloping algebra of Lie superalgebrasl(m,n)

Theq-deformations of the universal enveloping algebra ofsl(m, n) are considered, a Poincaré-Birkhoff-Witt type theorem is proved for these deformations, and the extra relations which are needed to definesl(m, n) as a contragredient algebra in addition to the Serre-type relations are identified with proof.     

Duality relations for asymmetric exclusion processes

We derive duality relations for a class ofU _q [SU(2)]-symmetric stochastic processes, including among others the asymmetric exclusion process in one dimension. Like the known duality relations for symmetric hopping processes, these relations express certainm-point correlation functions inN-particle systems (Nm) in terms of sums of correlation functions of the same system but with onlym particles. For the totally asymmetric case we obtain exact expressions for some boundary density correlation functions. The dynamical exponent for these correlators isz=2, which is different from the dynamical exponent for bulk density correlations, which is known to bez=3/2.     

Irrelevant operators and momentum-shell recursion relations ind=2 + ∈ dimensions

The momentum-shell recursion relations of Nelson and Pelcovits for ann-vector model near two dimensions are reexamined. The renormalization of the infinite set of relevant and marginal operators present in the system is studied. Ambiguities obtained in the ensuing recursion relations are shown to involve irrelevant operators only, thus justifying the procedure of Nelson and Pelcovits. The cases of finite external fieldh and finite spin anisotropyg are both considered.     

A two-parameter deformation of the universal enveloping algebra ofsl(3, C)

Starting from a certain multi-parameter matrix that satisfies the quantum Yang-Baxter equation, a two-parameter deformation of the universal enveloping algebra of the simple Lie algebrasl(3, C) is derived. It is shown that this has same product relations and antipode as the standard one-parameter deformationU _q(sl(3, C)) but has a different coproduct. It is also shown that there exists a Hopf algebra whose product relations are merely the commutation relations ofsl(3, C) itself, but whose coproduct is different from the usual one for the universal enveloping algebra ofsl(3, C).     

Hamiltonian formalism for non-invariant dynamics

In a completely Hamiltonian dynamical system, there will be a generating functionH _Y for each infinitesimal space-time transformationY. In the non-autonomous case, theH _Y depend on the observer. This dependence is here described by a system of commutation relations. It is also shown that these relations can be made to mirror exactly the commutation relations of theY's in the Lorentz-invariant case.The preparation of this paper was supported in part by NSF grant GP-33696X. It is a pleasure to acknowledge discussions with Professor H. Bacri, D. Kastler, J. M. Souriau and others at CNRS, CPT, Marseilles.     

Quaternion-Octonion SU(3) Flavor Symmetry

Starting with the quaternionic formulation of isospin SU(2) group, we have derived the relations for different components of isospin with quark states. Extending this formalism to the case of SU(3) group, we have considered the theory of octonion variables. Accordingly, the octonion splitting of SU(3) group have been reconsidered and various commutation relations for SU(3) group and its shift operators are also derived and verified for different isospin multiplets i.e. I, U and V-spins.     

Tighter Superadditivity Relations in Multiqubit Systems

Superadditivity relations characterize the distributions of coherence in multipartite quantum systems. In this work, we investigate superadditivity relations related to the l₁ norm of coherence \(\mathcal {C}_{l_{1}}\). Superadditivity relations for the αth power of \(\mathcal {C}_{l_{1}}\) have also been derived, which are gradually tighter for every multiqubit states.

     

Application of Partial Wave Crossing Relations to πN Scattering

The partial wave crossing relations derived in a recent paper by Steiner [1] are used for a calculation of the πN S-wave amplitudes in the region 8 ≦ s ≦ (M − 1)². The corresponding Argand diagrams show the pseudoresonance behaviour predicted in [1]. The results for the real parts are compared with an independent calculation using fixed-t dispersion relations.     

Relations at order p6 in chiral perturbation theory

We report on a search of relations valid at order p ⁶ in Chiral Perturbation Theory. We have found relations between π π, π K scattering, K _ℓ4 decays, masses and decay constants and scalar and vector formfactors. In this paper we give the relations and a first numerical check of them.     

Exactness of the Fock Space Representation of the <Emphasis Type="Italic">q</Emphasis>-Commutation Relations

We show that for all q in the interval (−1, 1), the Fock representation of the q-commutation relations can be unitarily embedded into the Fock representation of the extended Cuntz algebra. In particular, this implies that the C*-algebra generated by the Fock representation of the q-commutation relations is exact. An immediate consequence is that the q-Gaussian von Neumann algebra is weakly exact for all q in the interval (−1, 1).     

Uncertainty relation for successive measurements

It is noted that the Heisenberg uncertainty relations set a lower bound on the product of variances of two observablesA, B when they are separately measured on two distinct, but identically prepared ensembles. A new uncertainty relation is derived for the product of the variances of the two observablesA, B when they are measured sequentially on a single ensemble of systems. It is shown that the two uncertainty relations differ significantly wheneverA andB are not compatible.     

有限维奇偶对相干态的非经典性质

构造出了奇偶对相干态的指数形式, 并把奇偶对相干态推广至有限维Hilbert空间, 获得了有限维奇偶对相干态, 然后讨论了它们的正交归一完备性、反聚束效应和相位概率分布. 结果表明, 在此空间中奇偶对相干态具有归一完备性, 但不具有正交性. 借助于数值计算发现, 无论q取何值, 在参数|ξ|的不同取值范围内, 对于5维Hilbert空间中奇偶对相干态在模1和模2两个方向上均可呈现反聚束效应, 并且此双模光场的光子均是相关的. 而在7维Hilbert空间中，奇偶对相干态相位概率分 关键词： 有限维奇偶对相干态 反聚束效应 相位概率分布