The Characteristic Classes of Morita Equivalent Star Products on Symplectic Manifolds

In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of their characteristic classes: two star products ⋆ and ⋆' on (M,ω) are Morita equivalent if and only if there exists a symplectomorphism ψ\colon M M such that the relative class t(⋆, ψ^⋆(⋆')) is 2 π i-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's quantization condition for magnetic charges. Received: 19 July 2001 / Accepted: 23 January 2002     

On certain correspondences among various coupled-cluster theories for closed-shell systems

In this paper certain correspondences have been shown among various formulations of coupled-cluster theories for many electron closed-shell systems. Specifically it is shown that (i) the energy functional using unitary ansatz of the form exp (T−T ⁺) is exactly sameorder by order inT with the size-consistent energy functional 〈ψ|H|ψ〉/〈ψ|ψ〉 recently obtained by us in coupled-cluster framework; (ii) in the framework of unitary ansatz of the form exp (T−T ⁺), both non-variational and variational approaches lead to identical equations upto any given order inT andT ⁺ inT∼T ₂ approximation; (iii) variational procedure using our size-consistent energy functional or using the functional obtained in the framework of unitary ansatz (as envisaged by Kutzelnigg) leads to energy in both cases, inT∼T ₂ approximation, for a total of quadratic powers inT andT ⁺, same as Cizek’s linearised coupled pair many electron theory energy; (iv) in case of practical calculation of the energy through the variational procedures using our size-consistent energy functional and the functional in unitary ansatz framework, there is a loss of upper bound.     

Superparamagnetism in the 1D Ising model

The temperature dependence of the order parameter (〈M ²〉, the mean-square spin excess per spin) for a system with a finite number of spins of the 1D Ising model was investigated. It was shown that there is a nonzero temperature T _s below which 〈M ²〉 rapidly tends to unity. The analogy between the 1D ensemble of a finite number of spins and a system of superparamagnetic particles is discussed.     

q-quantum plane,ψ(q)-umbral calculus, and all that

It is known that one can formulateq-extended finite operator calculus with help of “quantumq-plane”q-commuting variablesA, B : AB − qBA ≡ [A, B]q=0. We shall recall this simple fact in its natural entourage which is the so-calledψ(q)-extension of Rota’s finite operator calculus. We aim to convince the audience that this is a natural and elementary method for formulation and treatment ofq-extended and possiblyR-extended orψ(q)-extended models for quantum-likeψ(q)-deformed oscillators. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001.     

<Emphasis Type="Italic">J</Emphasis>/<Emphasis Type="Italic">ψ</Emphasis> suppression and <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">T</Emphasis></Subscript> spectra in RHIC and LHC energy collisions

In a hydrodynamic model, we have studied J/ψ production in Au+Au/Cu+Cu collisions at RHIC energy, GeV. At the initial time, J/ψ’s are randomly distributed in the fluid. As the fluid evolves in time, the free streaming J/ψ’s are dissolved if the local fluid temperature exceeds a threshold temperature T _J/ψ . Sequential melting of charmonium states (χ _c , ψ ^′ and J/ψ), with melting temperatures , T _J/ψ ≈2T _c and feed-down fraction F≈0.3, explains the PHENIX data on the centrality dependence of J/ψ suppression in Au+Au collisions. J/ψ p _T spectra and the nuclear modification factor in Au+Au collisions are also well explained in the model. The model however overpredicts the centrality dependence of J/ψ suppression in Cu+Cu collisions by 20–30%. The J/ψ p _T spectra are underpredicted by 20–30%. The model predicts that in central Pb+Pb collisions at LHC energy,  GeV, J/ψ’s are suppressed by a factor of ∼10. The model predicted a J/ψ p _T distribution in Pb+Pb collisions at LHC is similar to that in Au+Au collisions at RHIC.     

Formation of charmonium states in heavy-ion collisions and thermalization of charm

We examine the possibility to utilize in-medium charmonium formation in heavy-ion interactions at collider energy as a probe of the properties of the medium. This is possible because the formation process involves recombination of charm quarks which imprints a signal on the resulting normalized transverse momentum distribution containing information about the momentum distribution of the quarks. We have contrasted the transverse momentum spectra of J/ψ, characterized by 〈p _T ²〉, which result from the formation process in which the charm quark distributions are taken at opposite limits with regard to thermalization in the medium. The first uses charm quark distributions unchanged from their initial production in a pQCD process, appropriate if their interaction with the medium is negligible. The second uses charm quark distributions which are in complete thermal equilibrium with the transversely expanding medium, appropriate if a very strong interaction between charm quarks and medium exists. We find that the resulting 〈p _T ²〉 of the formed J/ψ should allow one to differentiate between these extremes, and that this differentiation is not sensitive to variations in the detailed dynamics of in-medium formation. We include a comparison of predictions of this model with preliminary PHENIX measurements, which indicates compatibility with a substantial fraction of in-medium formation.     

Self-dual Maxwell field on a null surface. II

The canonical formalism for the Maxwell field on a null surface has been revisited. A new pair of gauge-independent canonical variables is introduced. It is shown that these variables are derivable from a Hamillon-Jacobi functional. The construction of the appropriate C ^* algebra is carried out in preparation for quantization. The resulting quantum theory is similar to a previous result. It is then shown that one can construct the T-variables of Rovelli and Smolin on the null surface. The Poisson bracket algebra exhibits causal relations along the null rays, but is nonsingular if the loops are restricted to those whose projections along the null rays are not tangent and one-to-one. Finally, there is a brief discussion of the relevance of this work to general relativity.It is a pleasure to dedicate this paper to Fritz Rohrlich who has been a collegue at Syracuse University for the past 30 years. We both came to Syracuse at the same time. Indeed, Fritz called me to induce me to do so at a time when I was still considering the move. I have never regretted following his lead.     

A Measurement of the ψ′ to J/ψ production ratio in 920?GeV proton-nucleus interactions

Ratios of the ψ^′ over the J/ψ production cross sections in the dilepton channel for C, Ti and W targets have been measured in 920 GeV proton-nucleus interactions with the HERA-B detector at the HERA storage ring. The ψ^′ and J/ψ states were reconstructed in both the μ⁺μ^- and the e⁺e^- decay modes. The measurements covered the kinematic range -0.35≤x_F≤0.1 with transverse momentum p_T≤4.5 GeV/c. The angular dependence of the ratio has been used to measure the difference of the ψ^′ and J/ψ polarization. All results for the muon and electron decay channels are in good agreement: their ratio, averaged over all events, is R_ψ′(μ)/R_ψ′(e)=1.00±0.08±0.04. This result constitutes a new, direct experimental constraint on the double ratio of branching fractions, (B^′(μ)B(e))/(B(μ)B^′(e)), of ψ^′ and J/ψ in the two channels. The ψ^′ to J/ψ production ratio is almost constant in the covered x_F range and shows a slow increase with p_T.     

Riesz Transforms on Deformed Fock Spaces

The Fock Von Neumann algebra , equipped with its canonical trace τ, is spanned by n hermitian operators acting on a Hilbert Fock space some commutation relations between and are defined by the n×n hermitian matrix A. We define a Riesz transform , where is the number operator, ∇^′ is aninner derivation (unbounded in general) and . Let 1<p<∞. We prove that is equivalent to for every with null trace, with constants which do not depend on n. Received: 24 November 1998 / Accepted: 2 March 1999     

Typicality of Pure States Randomly Sampled According to the Gaussian Adjusted Projected Measure

Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator ρ of low purity, tr ρ ² ≪1, and yielding the ensemble averaged expectation value tr (ρ A) for any observable A. Assuming that the given statistical ensemble ρ is generated by randomly sampling pure states |ψ〉 according to the corresponding so-called Gaussian adjusted projected measure (Goldstein et al. in J. Stat. Phys. 125:1197, 2006), the expectation value 〈ψ|A|ψ〉 is shown to be extremely close to the ensemble average tr (ρ A) for the overwhelming majority of pure states |ψ〉 and any experimentally realistic observable A. In particular, such a ‘typicality’ property holds  whenever the Hilbert space ℋ of the system contains a high dimensional subspace ℋ₊⊂ℋ with the property that all |ψ〉∈ℋ₊ are realized with equal probability and all other |ψ〉∈ℋ are excluded.     

Three-Point Functions for MN/SN Orbifolds¶with?= 4 Supersymmetry

The D1–D5 system is believed to have an “orbifold point” in its moduli space where its low energy theory is a ?=4 supersymmetric sigma model with target space M ^N /S _N , where M is T ⁴ or K3. We study correlation functions of chiral operators in CFTs arising from such a theory. We construct a basic class of chiral operators from twist fields of the symmetric group and the generators of the superconformal algebra. We find explicitly the 3-point functions for these chiral fields at large N; these expressions are “universal” in that they are independent of the choice of M. We observe that the result is a significantly simpler expression than the corresponding expression for the bosonic theory based on the same orbifold target space. Received: 29 March 2001 / Accepted: 20 January 2002     

All Stable Characteristic Classes of Homological Vector Fields

An odd vector field Q on a supermanifold M is called homological, if Q ² = 0. The operator of Lie derivative L _Q makes the algebra of smooth tensor fields on M into a differential tensor algebra. In this paper, we give a complete classification of certain invariants of homological vector fields called characteristic classes. These take values in the cohomology of the operator L _Q and are represented by Q-invariant tensors made up of the homological vector field and a symmetric connection on M by means of the algebraic tensor operations and covariant differentiation.     

Schrödinger Operators and the Zeros of Their Eigenfunctions

In n-dimensional Euclidean space let us be given an infinitely differentiable real valued function V that is bounded below. We associate with the formal operator that sends a complex valued function ψ into −div(grad ψ) + V ψ a uniquely defined self adjoint operator which we will denote by −Δ + V.     

Logarithmic Intertwining Operators and Vertex Operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg and lattice vertex algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1) _a , of central charge 1 − 12a ². We classify these operators in terms of depth and provide explicit constructions in all cases. Our intertwining operators resemble puncture operators appearing in quantum Liouville field theory. Furthermore, for a = 0 we focus on the vertex operator subalgebra L(1, 0) of M(1)₀ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of hidden logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1, 0)-module.     

Method of Quantum Characters in Equivariant Quantization

 Let G be a reductive Lie group, g its Lie algebra, and M a G-manifold. Suppose 𝔸 _h (M) is a 𝕌 _h (g)-equivariant quantization of the function algebra 𝔸(M) on M. We develop a method of building 𝕌 _h (g)-equivariant quantization on G-orbits in M as quotients of 𝔸 _h (M). We are concerned with those quantizations that may be simultaneously represented as subalgebras in 𝕌^* _h (g) and quotients of 𝔸 _h (M). It turns out that they are in one-to-one correspondence with characters of the algebra 𝔸 _h (M). We specialize our approach to the situation g=gl(n,ℂ), M=End(ℂ ⁿ ), and 𝔸 _h (M) the so-called reflection equation algebra associated with the representation of 𝕌 _h (g) on ℂ ⁿ . For this particular case, we present in an explicit form all possible quantizations of this type; they cover symmetric and bisymmetric orbits. We build a two-parameter deformation family and obtain, as a limit case, the 𝕌(g)-equivariant quantization of the Kirillov-Kostant-Souriau bracket on symmetric orbits. Received: 28 April 2002 / Accepted: 3 October 2002 Published online: 24 January 2003 RID="*" ID="*" This research is partially supported by the Israel Academy of Sciences grant no. 8007/99-01. Communicated by L. Takhtajan     

Radiative decays,photoproduction and total cross section of theψ particles

It is pointed out that the coupling characterizing theψ-γ vertex must change substantially between the limits,ψ on mass-shell which occurs inψ→e ⁺ e ⁻ and photon on mass-shell which is relevant in radiative decays likeψ→ππγ, ψ→ηγ and photoproduction ofψ. This has the consequence that the value ofψN total cross section must be larger than what is inferred from the use of naive vector dominance in photoproduction.     

The 2<Superscript>1/3</Superscript> rule for magnetic susceptibility of gadolinium

The dependences of the magnetization M and the magnetic susceptibility χ = ∂M/∂H of pure gadolinium (the concentration of foreign impurities is lower than 0.1 wt %) on the temperature T and the magnetic field H have been measured using a Quantum Design MPMS-5XL SQUID magnetometer. In this material, inhomogeneities of the atomic structure should not lead to a nonuniform distribution of the magnetic characteristics (including the Curie temperature T _C) over the volume of the sample. The obtained dependences of M and χ have been used to investigate the possibility of suppressing magnetic inhomogeneities of other types by magnetic fields with a strength of up to 50 kOe. It has been assumed that these inhomogeneities are suppressed when the specific relationship, namely, the 2^1/3 rule is fulfilled. The rule relates the portions of the dependence χ(T, H) which at the temperature T = T _C and at the maximum in the curve χ(T) (T = T _m ) depend on H in accordance with the H ^2/3 law. It has been shown that the portions separated from the experimental curves χ(T _C, H) and χ(T _m , H) obey the 2^1/3 rule.     

Weighted Bergman Kernels and Quantization}

Let Ω be a bounded pseudoconvex domain in C ^N , φ, ψ two positive functions on Ω such that − log ψ, − log φ are plurisubharmonic, and z∈Ω a point at which − log φ is smooth and strictly plurisubharmonic. We show that as k→∞, the Bergman kernels with respect to the weights φ ^{k ψ} have an asymptotic expansion

Twisted Sectors for Tensor Product Vertex Operator Algebras Associated to Permutation Groups

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V ^{⊗ k} . We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the tensor product vertex operator algebra V ^{⊗ k} are isomorphic to the categories of weak, weak admissible and ordinary V-modules, respectively. The main result is an explicit construction of the weak g-twisted V ^{⊗ k} -modules from weak V-modules. For an arbitrary permutation automorphism g of V ^{⊗ k} the category of weak admissible g-twisted modules for V ^{⊗ k} is semisimple and the simple objects are determined if V is rational. In addition, we extend these results to the more general setting of γg-twisted V ^{⊗ k} -modules for γ a general automorphism of V acting diagonally on V ^{⊗ k} and g a permutation automorphism of V ^{⊗ k} . Received: 20 April 2000 / Accepted: 20 January 2002     

Higher order differential lift equations over manifolds

LetM be a differentiable manifold modeled on a Banach space overK=R or C. LetT ^k(M) be thekth iterated tangential extension ofM, and letk ^M be thekth Bowman (=restricted tangential) extension ofM. It is shown that there is an embedding ϕ_k:k ^{→T k}(M), and that such embeddings constitute a natural transformation of functors. LetQ be a subset/submanifold inT ^k(M), and letV:Q→T(Q) be a differentiable vector field. CallV k-suitable if everyK-curveg inQ satisfyingg′=V° g has the formg=f ^[k], wheref ^[k] denotes thekth iterated differential lift of aK-curvef inM. It is shown thatV isk-suitable if and only if: (a) , where is a subset/submanifold ink ^M, and (b) , where isk-suitable relative to restricted tangentialK-curve liftsf ^(k). Interpretive consequences for motion problems are discussed.