On the distributions corresponding to bounded operators in the Weyl quantization

Using properties of an integral transform giving directly the matrix elements of a quantum mechanical operator from the corresponding classical function, we restrict the class of distributions corresponding to bounded operators. As a consequence, we can exhibit a class of functions yielding trace-class operators, and give a bound on their trace-norm.Wetenschappelijk medewerker bij het Interuniversitair Institut voor Kernwetenschappen (in het kader van het navorsingsprojekt 21 EN)     

On Laguerre polynomials and the convolution product of parabolic cylinder functions

We compute the convolution product of a pair of parabolic cylinder functions of integer non-negative indices and express the result in terms of Laguerre polynomials. Symmetry properties, recurrence formulas and physical applications of such products as well as some of their generalizations are also investigated.     

A guided tour of new tempered distributions

Laurent Schwartz, the principle architect of distribution theory, presented the impossibility of extending a form of multiplication to distribution theory. There have been many varieties of partial solutions to this problem. Some of the solutions contain heuristic computations done by physicists in quantum field theory. A recent strategy developed by J. Colombeau culminates with multiplication and integration theory for distributions. This paper develops this theory in the spirit of a sequence approach, much like fundamental sequences are to distributions. However, in the new tempered distribution theory the sequences can be noncountable. T. Todorov developed these techniques for new distributions. However, since so many applications require Fourier analysis, the new tempered distributions provide a natural setting for physics and signal analysis. The paper illustrates the product of two Dirac delta functionals,(x)(x). Other nonregular distributional products can also be computed in the same manner. The paper culminates with a new application of annihilation and creation operators in quantum field theory.     

Weyl anomaly of the product of string vertex functions

In the Polyakov's path integral formalism we calculate the Weyl anomaly of the product of vertex functions which emit the oscillation modes of closed bosonic string. This Weyl anomaly appears when several strings' emission points on the world sheet approach to the same point. Owing to this anomaly, Weyl invariance in the presence of background fields determines the background field equations of motion.     

s-parameterized Weyl transformation and the corresponding quantization scheme

By extending the usual Weyl transformation to the s-parameterized Weyl transformation with s being a real parameter,we obtain the s-parameterized quantization scheme which includes P–Q quantization,Q–P quantization,and Weyl ordering as its three special cases.Some operator identities can be derived directly by virtue of the s-parameterized quantization scheme.     

On the Weyl Ordering operation

A Weyl ordering product operation (with its representative symbol) is introduced. On the basis of the operation, a technique of integration within a Weyl ordered product is put forward. Application of the technique to the coherent state representation leads us to derive the Weyl ordered forms of some important operators in quantum mechanics, which can be rigorously checked by the relation between our Weyl ordering product operation and the Weyl correspondence rule.     

On the Weyl curvature hypothesis

The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity.     

On the notion of Weyl system

We review the standard notion of Weyl system, which stems from the Weyl formulation of the canonical commutation relations of quantum mechanics, and propose an alternative definition based on the theory of projective representations. Next, we discuss some conceptual advantages of this alternative definition. Finally, we introduce a notion of physical equivalence of group representations and propose a further ‘purely conceptual’ definition of Weyl system based on this notion.     

On dual properties of the Weyl tensor

We present some new identities satisfied by double and triple products of the Weyl tensorW _v and its dual .Partially supported by C.N.Pq.     

On the Weyl Representation of Metaplectic Operators

We study the Weyl representation of metaplectic operators associated to a symplectic matrix having no non-trivial fixed point, and justify a formula suggested in earlier work of Mehlig and Wilkinson. We give precise calculations of the associated Maslov-type indices; these indices intervene in a crucial way in Gutzwiller’s formula of semiclassical mechanics, and are simply related to an index defined by Conley and Zehnder.     

On the Newtonian limit of the Weyl tensor

In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and magnetic parts of the Weyl tensor. We also discuss that only a subset of the relativistic equations is needed to obtain a closed system of equations in the Newtonian limit.     

On an Alignment Condition of the Weyl Tensor

We generalize an alignment condition of the Weyl tensor given by Barnes and Rowlingson. The alignment condition is then applied to Petrov type D perfect fluid spacetimes. In particular, purely magnetic, Petrov type D, shear-free perfect fluids are shown to be locally rotationally symmetric.     

A convolution formula for a phase transition of hadronic matter and the multiplicity distributions

We propose a general form for the statistical bootstrap equation by means of a convolution formula for the thermodynamical system of hadronic matter. In connection with a phase transition of hadronic matter to a state of quark liberation, we predict the negative binomial distribution with k∼1 for the multiplicity distributions in the central pseudorapidity region at high energies.     

On higher-order coherent states of the Weyl algebra

It is shown that for classical, analytical states of the Weyl algebra, the quantum optical coherence condition of second order implies those of nth order for all n2.     

On the transition from Weyl to Ricci focusing

Using the weak-field approximation, we show that the Weyl focusing of rays in a beam of light which passes around a number of spherical deflectors may be approximated by the Ricci focusing of the beam due to the enclosed mass.     

On entropies and temperature parameters characterizing product distributions in chemical reactions and corresponding thermodynamic quantities

The relations between the entropy (information content) and temperature parameters characterizing non-relaxed product distributions in chemical reactions and thermodynamic quantities are demonstrated. Two cases of initial reactant distributions—state-selected and thermal—are considered. The entropy change in the passage from non-equilibrium product distributions to partially relaxed distributions and the connection between the two kinds of vibrational temperatures characterizing these stages are treated in detail. An actual ‘entropy cycle’ is described.     

扭转对称光束的产生及其变换过程中的轨道角动量传递

研究了采用扭转柱面镜光学系统将厄米-高斯光束变换成为具有轨道角动量的拉盖尔-高斯扭转对称光束. 采用本征模式分解的方法分析了扭转柱面镜光学变换系统实现光束变换的原理.利用光束传输矩阵和二阶矩理论分析计算了光束经过扭转柱面透镜变换过程中的轨道角动量传递过程，证明光束与透镜系统的轨道角动量交换发生在第一个柱面透镜处，光束经过第一个柱面透镜后，具有的轨道角动量保持不变. 关键词： 轨道角动量 光束变换 扭转对称光束 轨道角动量传递