bluuebunny/crossref_metadata_2025 huggingface dataset:
Cluster isolated chemical reaction (CICR) spectroscopy: Ba atoms and Ba(CH4)n complexes on large neon clusters
Authors: Briant M. , Gaveau M. A. , Mestdagh J. M. , Visticot J. P.
Published: July 2002

The cluster isolated chemical reaction (CICR) technique was applied to neon clusters (Ne≈7000) on which barium atoms and methane molecules were deposited. Clusters carrying barium only were studied first. Qualitatively, the present results on neon clusters are in line with our previous results on argon clusters. In particular, surface location of barium was observed. The central part of the present work concerns neon clusters carrying both one barium atom and one to ten methane molecules. Several types of spectroscopy were performed in the region of the resonance transition (6s2)1S→(6s6p)1P of barium (excitation spectrum of the total fluorescence, emission spectrum, action spectrum for forming (6s6p)3P), and experiments where the number of methane molecules per cluster, which was strictly controlled, was varied systematically. The corresponding results were interpreted on the ground of a model, which transposes both chemical thermodynamics of equilibria and reaction kinetics to CICR experiments. Such an approach has a strong relationship, although it is more simple, with the thermodynamical approach to reactions in micellar solutions. The present thermodynamical model helped us to determine the origin of the action spectrum for forming Ba(6s6p)3P in clusters carrying both one barium atom and an average of 2.5 methane molecules. This action spectrum was assigned to direct excitation of the Ba(CH4) and Ba(CH4)2 complexes. The present thermodynamical model was also applied to our former results on argon clusters. This allowed us to derive a consistent picture of the association reaction of barium with methane and of the quenching of electronic excitation of barium by methane in both environments.
The effect of cluster formation on mass separation in binary molecular beams
Authors: Li Wei , Stirniman M. J. , Sibener S. J.
Published: July 2002

The downstream composition of a skimmed supersonic binary molecular beam originally consisting of a 20% neon/80% xenon mixture before expansion has been studied as a function of nozzle stagnation pressure. We have found that the neon to xenon ratio dropped dramatically as the stagnation pressure was increased at low nozzle temperature (303 K), a drop which cannot be well described by existing theory. Time-of-flight (TOF) measurements indicate that Xe clustering occurs as the stagnation pressure is increased. This clustering coincides with the additional Ne depletion we observe. At a higher nozzle temperature where Xe clustering does not occur (573 K), this measured mass separation phenomenon is absent. Similar experiments have been done for another binary mixture, 20% O2/80% Xe. Similar anomalous mass separation is observed with this mixture, confirming the attribution of this phenomenon to clustering of the more massive component of the mixture. These findings have implications for novel methods of gas-dynamics-based mass separation potentially including isotope enrichment.
Are properties derived from variance-optimized wave functions generally more accurate? Monte Carlo study of non-energy-related properties of H2, He, and LiH
Authors: Snajdr Martin , Rothstein Stuart M.
Published: July 2002

It is commonly believed that variance-optimized wave functions yield “satisfactory” if not, in principle, better estimates of non-energy-related physical properties than their energy-optimized counterparts. We test this notion by calculating a number of ground-state physical properties using a variety of variance- and energy-optimized wave functions for He, H2, and LiH. We gauge the quality of the properties using as a “metric” the sum of absolute relative errors. Our results suggest that the energy-optimized wave functions consistently provide better estimates of non-energy-related properties than variance-optimized ones. We present qualitative arguments supporting these findings.
The spectra and the relative yield of solvated electrons produced by resonant photodetachment of iodide anion in ethylene glycol in the temperature range 296⩽T⩽453 K
Authors: Chandrasekhar N. , Krebs P.
Published: July 2002

We have produced solvated electrons (esolv−) in ethylene glycol (EG) by irradiation of a 248 nm laser pulse in the charge-transfer-to-solvent (CTTS) band of I− (resonant photodetachment). We report on the optical absorption spectra of esolv− as a function of temperature. A red-shift of the position of the absorption maximum, Δℏωmax≈−0.4 eV, corresponding to d(ℏωmax)/dT=−(2.49±0.07)×10−3 eV K−1 in the temperature range 296⩽T⩽453 K is reported. The observed absorbance of esolv− at ℏωmax increases by a factor of about 60 when the temperature is increased from 296 to 453 K. This effect can be explained only partially by the favorable red-shift of the CTTS spectrum of I− with respect to the laser wavelength by increasing the temperature. The self diffusion coefficient in EG is by a factor of 25 lower than in water at 298 K and increases strongly with temperature. It is concluded that a reaction step with a diffusion controlled escape probability for the electron determines the yield of esolv−. The results are, therefore, analyzed according to a simple kinetic model proposed by Staib and Borgis [J. Chem. Phys. 104, 9027 (1996)].
Infrared spectra and theoretical studies of the C2O3− anion isolated in solid argon
Authors: Zhou Mingfei , Zhang Luning , Chen Mohua , Qin Qizong
Published: July 2002

Laser ablation of transition metal targets with concurrent 11 K deposition of CO2/CO/Ar mixtures produces CO2− anion absorption at 1657.0 cm−1 and two additional metal independent absorptions at 1793.7 and 1701.7 cm−1. Isotopic substitution shows that the 1793.7 cm−1 band is due to a C–O stretching vibration and the 1701.7 cm−1 band an antisymmetric CO2 vibration. The UV photolysis and CCl4 doping experiments strongly suggest an anion identification. Based on density functional theory and ab initio calculations of structure and vibrational frequencies, these two bands are assigned to the C–O and antisymmetric CO2 stretching vibrations of the C2O3− anion coordinated between two C atoms with nonplanar Cs symmetry. Our calculations also show that the C2O3− anion is a covalently bound molecule.
Accurate and approximate calculations of Franck–Condon intensities in the carbon 1s photoelectron spectrum of methane
Authors: Karlsen Tor , Bo/rve Knut J.
Published: July 2002

The level of theory needed in order to accurately compute the bond contraction following core ionization in methane is examined with an emphasis on one-electron bases and treatment of electron correlation. At our highest level of theory, including core–valence electron correlation, a value of 4.82 pm is computed for the bond contraction in core-ionized methane, in good agreement with experimental findings. The associated potential energy curve in the symmetric stretching coordinate is used to form relative intensities of the peaks in the C 1s photoelectron spectrum of methane. For use in more approximate studies, it is proposed that the ionized core may be conveniently represented by effective core potentials during geometry optimization, and the prospect of this approach is explored in some depth.
On the independence of nonadiabatic coupling elements on the choice of origin of the coordinate system
Authors: Buenker Robert J. , Li Yan
Published: July 2002

A finite-difference approach is employed to demonstrate the manner in which the values of nonadiabatic radial coupling matrix elements vary with the choice of origin of the nuclear coordinate system. Configuration interaction (CI) calculations for a series of excited states of the HCl molecule verify that such results do not depend on the location of the center of mass XCM as long as it is held fixed during the differentiation process. The reason that radial coupling matrix elements are found to vary with the choice of origin of the coordinate system in standard scattering formulations is that the corresponding motion is not purely internal but rather has a definite translational component, namely a linear dependence of XCM on the bond distance R is assumed. An identity which relates variations of such (mixed internal-translational motion) nonadiabatic coupling elements to the value of the electric dipole transition moment when the latter prescription is employed for choosing the origin of the nuclear coordinate system is also verified by the present CI calculations.
Linear dynamic Kerr effect response of polar molecules in coupled ac and dc bias fields: Account of inertial effects via the J-diffusion model
Authors: Déjardin P. M.
Published: July 2002

The dynamic Kerr response of noninteracting rigid polar linear molecules in superimposed strong dc and weak ac electric fields including inertial effects is investigated. The calculations are carried out for rotation in space in the context of linear response theory for the extended rotational (J-diffusion) model and extend the results of previous work. The birefringence spectrum is evaluated for typical values of the model parameters. Simple analytical equations for the spectrum are obtained for the limiting cases of rare and frequent collisions. The limit of frequent collisions allows us to compare the J-diffusion model with the Fokker–Planck model in the overdamped limit, where the inertial effects are neglected. It is found just as in dielectric relaxation that the birefringence relaxation times are very similar for the two models, but not identical. Also a crossover region between the low and high damping limits is exhibited by the Kerr effect relaxation time just as in Kramers’ escape rate theory. In addition, this crossover region is shifted to higher friction parameter values when the applied dc field is increased. A comparison with previous theories is given.
Ab initio studies on the low-lying excited states of ClO3 and BrO3
Authors: Li Yumin , Francisco Joseph S.
Published: July 2002

The vertical excitation energies and the transition moments of the ClO3 and BrO3 states, 1 2A1, 1 2A2, 1 2E, and 2 2E, are calculated at the complete active space self-consistent field (CASSCF), multi-reference configuration interaction (MRCI), and complete active space self-consistent field with second-order perturbation correction (CASPT2) levels of theory. The basis sets, cc-pVTZ and aug-cc-pVTZ, are used for ClO3, and cc-pVTZ and TZ2P (2sp) are used for BrO3. The potential energy curves for the states studied are computed at the CASSCF level of theory with the cc-pVTZ basis set. The differences and similarities between the ClO3 and BrO3 states are examined. Results for ClO3 are found to be consistent with recent UV experiment results that are used to characterize the ClO3 radical.
Dynamic lattice Monte Carlo simulation of a model protein at an oil/water interface
Authors: Anderson Rebeccah E. , Pande Vijay S. , Radke Clayton J.
Published: July 2002

Adsorption of a proteinlike heteropolymer is modeled at an oil/water interface by dynamic lattice Monte Carlo simulation. The heteropolymer is a designed sequence of 27 amino-acid-type lattice sites and has been used as a model for short (50–70) residue proteins. Oil is represented by a characteristic hydrophobic amino acid monomer, and water is represented by a characteristic hydrophilic amino acid monomer. The model protein is initially placed slightly away from the oil/water interface and is then allowed to undergo Verdier–Stockmeyer moves as amino acid sites interact with each other and with the oil and water. Local mixing of the oil and water is permitted over the length scale of the protein. Our lattice representation displays correct behavior in bulk water in that the model protein folds rapidly from an extended rod into a globular like state. In addition, there is a phase transition between the globular (folded) state and the denatured (unfolded) state at a particular temperature, Tm*. By examining the free-energy landscape at 0.94 Tm*, we identify four configurational states in the adsorbing system: unfolded in the bulk water, folded in the bulk water, unfolded at the interface, and folded at the interface. The most probable state of the four is the adsorbed unfolded state at the interface, with a large free-energy barrier to desorption. (∼20 kBTm*). We find that it is the unfavorable interaction between the oil and the water that drives the protein to the interface. Adsorption of a single protein molecule reduces the oil and water energies by 175 kBTm*. A typical conformation of the adsorbed, unfolded protein has the majority of protein segments remaining in the water but lying directly adjacent to the interface, with about 30% loops penetrating into the water phase and only a few segments (∼10%) penetrating into the oil. This work provides a picture of single-molecule protein adsorption at the oil/water interface in which the protein unfolds into an extended train structure and thereafter is essentially irreversibly bound.
Quantum reactive scattering in three dimensions: Using tangent-sphere coordinates to smoothly transform from hyperspherical to Jacobi regions
Authors: Parker Gregory A. , Keil Mark , Morrison Michael A. , Crocchianti Stefano
Published: July 2002

Hyperspherical coordinates are well suited for treating rearrangement processes in the strong interaction region, and several different hyperspherical coordinates have been used successfully for quantum reactive scattering by various research groups. However, it is well known that asymptotically the appropriate set of coordinates (for a three particle system) are the three sets of Jacobi coordinates. In this paper we show how one can smoothly connect the hyperspherical coordinates in the rearrangement region to Jacobi coordinates in the nonrearrangement region using tangent-sphere coordinates. This procedure reduces the computational time required to solve the quantum Schrödinger equation and eliminates the need for numerical projection. To illustrate this method, we apply it to the F+H2⇌HF+F reaction, comparing reaction probabilities to those from previous benchmark calculations based on a conventional formulation.
Collision induced fragmentation of small ionic sodium clusters. II. Three-body fragmentation
Authors: Barat M. , Brenot J. C. , Dunet H. , Fayeton J. A. , Picard Y. J.
Published: July 2002

Multiple fragmentation of small Nan+ clusters (n=3–5) induced by collision with He atoms is investigated in the 200 eV collision energy range. The Nan+→Nan−2++Na+Na channels are studied using a multicoincidence technique allowing for the determination of the velocity vectors of the three fragments. The relative contributions of the two basic mechanisms, namely the electronic excitation and the momentum transfer in elastic binary collisions between the He atom and a Na core are estimated. For Na4+ and Na5+ clusters the momentum transfer mechanism appears as a two-step process: The ejection of a fast Na atom in a binary Na–He collision followed by the evaporation of an additional slow Na atom. However the angular distribution of the slow Na atom is not isotropic showing that a partial memory of the initial binary collision appears in the evaporation process.
Generalization of Weyl’s gauge group
Authors: Komar Arthur
Published: July 2002

Weyl’s gauge transformations in a general n-dimensional Riemannian manifold are extended from the conformal group to GLn(R). The gauge-covariant field generalizing that of the Maxwell tensor is determined. The relationship between Weyl gauging and Yang–Mills gauging is developed. It is shown that the two processes are not equivalent, but can be made compatible.
Schrödinger semigroups for vector fields
Authors: Osborn T. A. , Corns R. A. , Fujiwara Y.
Published: July 2002

Suppose H is the Hamiltonian that generates time evolution in an N-body, spin-dependent, nonrelativistic quantum system. If r is the total number of independent spin components and the particles move in three dimensions, then the Hamiltonian H is an r×r matrix operator given by the sum of the negative Laplacian −Δx on the (d=3N)-dimensional Euclidean space Rd plus a Hermitian local matrix potential W(x). Uniform higher-order asymptotic expansions are derived for the time-evolution kernel, the heat kernel, and the resolvent kernel. These expansions are, respectively, for short times, high temperatures, and high energies. Explicit formulas for the matrix-valued coefficient functions entering the asymptotic expansions are determined. All the asymptotic expansions are accompanied by bounds for their respective error terms. These results are obtained for the class of potentials defined as the Fourier image of bounded complex-valued matrix measures. This class is suitable for the N-body problem since interactions of this type do not necessarily decrease as ‖x‖→∞. Furthermore, this Fourier image class also contains periodic, almost periodic, and continuous random potentials. The method employed is based upon a constructive series representation of the kernels that define the analytic semigroup {e−zH‖Re z>0}. The asymptotic expansions obtained are valid for all finite coordinate space dimensions d and all finite vector space dimensions r, and are uniform in Rd×Rd. The order of expansion is solely a function of the smoothness properties of the local potential W(x).
Color analysis, theory of Γ-graded integrable evolution equations, and super Nijenhuis operators
Authors: Trostel Robert
Published: July 2002

Using the generalized Grassmann variables or color variables, a theory of Γ-graded integrable evolution equations is presented by elevating the treatments of Magri, Gel’fand–Dorfman, and Fuchssteiner of nonlinear integrable bosonic evolution equations to the Γ-graded case. As an example, it is shown that Kupershmidt’s super-KdV is characterized by a Z2-graded Nijenhuis operator compatible with the underlying Z2-graded Hamiltonian structure.
The group of gauge transformations as a Schwartz–Lie group
Authors: Cirelli Renzo , Manià Alessandro
Published: July 2002

The group of gauge transformations of a smooth principal bundle P(M,G) over a not necessarily compact manifold M and with a not necessarily compact structure group G is proved to be a Schwartz–Lie group. Its Lie algebra and exponential map are discussed.
The Green’s function for a finite linear chain
Authors: Bass Ronald
Published: July 2002

A new expression for the Green’s function of a finite-length one-dimensional harmonic lattice with nearest-neighbor interactions is reported. Simple closed expressions in terms of Chebyshev polynomials are developed for periodic, fixed, and free end boundary conditions.
Geometrical interpretation of the solutions of the sine–Gordon equation
Authors: Klein J. J.
Published: July 2002

The sine–Gordon equation is known to possess solutions that correspond to solitons, that is, localized entities that maintain their shape after collisions, and have certain properties characteristic of elementary particles. Although the algebraic structure of these solutions is well known, their geometric interpretation as surfaces of constant negative curvature has not been previously illuminated. We discuss these surfaces herein. Curves drawn on these surfaces along the asymptotic directions at each point simulate solutions of the nonlinear wave equation φxx−φtt=sin φ.
The state labeling problem—A universal solution
Authors: Coleman A. J.
Published: July 2002

A new method is proposed for labeling a basis for any irreducible representation, with top weight, of a simple Lie algebra (LA). It has two advantages over Gel’fand–Zetlin patterns: (i) being exactly the same for all LA’s both exceptional and classical and (ii) providing labels that are much more compact. Thus it may prove useful in discussing large representations such as those E8⊗E8 that occur in superstring theory. The method makes essential use of the Weyl group and is based on a theorem that associates to each weight a symmetric matrix with integer coefficients whose rank equals the multiplicity of the weight.
Multiplicity-free Wigner coefficients for semisimple Lie groups. II. A pattern calculus for O(n)
Authors: Gould M. D.
Published: July 2002

In this paper a direct, algebraic derivation of a large class of (multiplicity-free) reduced Wigner coefficients is presented for the orthogonal groups. In particular all elementary reduced Wigner coefficients, including those for the fundamental spinor and tensor representations, are obtained. The results are presented in a form directly analogous to the corresponding results obtained for the unitary groups.
Infinite hierarchies of t-independent and t-dependent conserved functionals of the Federbush model
Authors: Kersten P. H. M. , Ten Eikelder H. M. M.
Published: July 2002

The construction of four infinite hierarchies of t-independent and t-dependent conserved functionals for the Federbush model is given. A formal proof of the existence of these infinite hierarchies is given in Appendix B.
Non-Abelian Aharonov–Bohm effects, Feynman paths, and topology
Authors: Sundrum Raman , Tassie L. J.
Published: July 2002

The Aharonov–Bohm effect in general gauge theories, for particles in gauge-curvature-free regions, is studied using the quantum mechanical propagator in the form of a Feynman sum over paths. Following Schulman [L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981)], such paths are divided into their homotopy equivalence classes, and the contributions from each class of paths of the Feynman sum are identified with propagators of a wave equation in the universal covering manifold of M, resulting in a simple form for the propagator on M. A group homomorphism from ℋ, the fundamental homotopy group of M, to the gauge group G is shown to characterize possible Aharonov–Bohm effects, which can be divided into two types, Abelian and non-Abelian, according to whether ℋ*, the image of this homomorphism, is Abelian or non-Abelian. For a non-Abelian Aharonov–Bohm effect, it is necessary that both ℋ and G be non-Abelian. Simple examples illustrate the theory.
Transmission through a system of potential barriers. II. Necessary condition for complete transparency. A maximum transmission problem
Authors: Dammert Örjan
Published: July 2002

A smooth one-dimensional system of N potential barriers of arbitrary shapes (unequal or equal) is considered. A general necessary condition for complete transparency is obtained that can be understood as a constraint on the reflection coefficients pertaining to the single barriers of the system. A maximum transmission problem of a general kind is solved and the solution is used to give a physical interpretation of the necessary condition. The sub- and superbarrier cases are treated in a unified way. The exact final formulas can readily be converted into accurate approximate ones by insertion of available phase-integral expressions (of an arbitrary order) for certain characteristic quantities appearing in the formulas.
Parametrization of the linear zeros of 6j coefficients
Authors: Labarthe J. J.
Published: July 2002

The linear zeros of 6j coefficients are fully parametrized apart from a multiplicative factor in terms of four integers.
Tree graphs and the solution to the Hamilton–Jacobi equation
Authors: Molzahn F. H. , Osborn T. A.
Published: July 2002

A combinatorial method is used to construct solutions of the Hamilton–Jacobi equation. An exact expression for Hamilton’s principal function S is obtained for classical systems of finitely many particles interacting via a certain class of time-dependent potentials. If x, p, and t are the position, momentum, and time variables for N point particles of mass m, it is shown that Hamiltonians of the form H(x,p,t)=(1/2m)p2+v(x,t) have complete integrals S that are analytic functions of the inverse mass parameter m−1 in a punctured disk about the origin. If v(x,t) is bounded, C∞ in the x variable, and has controlled x-derivative growth, then the coefficients of the Laurent expansion of S about m−1=0 may be expressed in terms of gradient structures associated with tree graphs. This series expansion for S(x,t; y,t0) converges absolutely, and uniformly for all x, y for time displacements ‖t−t0‖<T≡2K−1(m/eU)1/2, where K and U are bounds associated with the space derivatives of the potential. For ‖t−t0‖<T, the classical path (from any initial space-time configuration y,t0 to any final configuration x,t) induced by S is unique, passes through no conjugate points, and furnishes the action functional with a strong minimum. The local solution S given above may be used to obtain the classical trajectories for arbitrarily large times.
On the theory of one-parameter subgroups of supergroups
Authors: Truax D. Rodney , Kostelecký V. Alan , Nieto Michael Martin
Published: July 2002

The one-parameter subgroups of supergroups are defined and their primary properties are delineated. Parametrization schemes analogous to those used in Lie group theory are investigated. In particular, exponentiation is introduced and related to the one-parameter subgroups. Canonical coordinates of three kinds are investigated, the third of which has no analog in conventional Lie theory. We illustrate our results with the examples of the supersymmetric quantum-mechanical superalgebra sqm(2) and the simple superalgebra osp(1/2).
Geometrical properties of the algebraic spinors for R3,1
Authors: Bugajska Krystyna
Published: July 2002

The different geometrical properties of Majorana, ‘‘even,’’ Dirac, and Chevalley spinors in the Clifford algebra approach are investigated.
Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles
Authors: Del Olmo M. A. , Rodríguez M. A. , Winternitz P.
Published: July 2002

Nonlinear ordinary differential equations admitting a superposition principle based on the action of the group SL(n,C) on the homogeneous spaces SL(n,C)/O(n,C) and SL(n,C)/Sp(n,C) are derived. The superposition formulas are presented explicitly. In the O(n,C) case the general solution is expressed in terms of three particular solutions (for any n). For the Sp(n,C) case three solutions are needed for n=2k≥8, four solutions for n=6, and five solutions for n=4.
Cosmological models in globally geodesic coordinates. II. Near-field approximation
Authors: Hongya Liu
Published: July 2002

A near-field approximation dealing with the cosmological field near a typical freely falling observer is developed within the framework established in the preceding paper [J. Math. Phys. 28, xxxx(1987)]. It is found that for the matter-dominated era the standard cosmological model of general relativity contains the Newtonian cosmological model, proposed by Zel’dovich, as its near-field approximation in the observer’s globally geodesic coordinate system.
Semiclassical treatment of spin system by means of coherent states
Authors: Solari Hernán G.
Published: July 2002

The semiclassical time-dependent propagator is studied in terms of the SU(2) coherent states for spin systems. The first- and second-order terms are obtained by means of a detailed calculation. While the first-order term was established in the earlier days of coherent states the second-order one is a subject of contradiction. The present approach is developed through a polygonal expansion of the discontinuous paths that enter the path integral. The results here presented are in agreement with only one of the previous approaches, i.e., the one developed on Glauber’s coherent states by means of a direct WKB approximation. It is shown that the present approach gives the exact result in a simple case where it is also possible to observe differences with previous works.
On the problem of local hidden variables in algebraic quantum mechanics
Authors: Rédei Miklós
Published: July 2002

Given two Bose-type quasilocal C*-algebras 𝒜, ℬ, their state spaces E(𝒜), E(ℬ), and a positive, unit preserving map L: ℬ→𝒜, respecting the local structure of 𝒜 and ℬ (𝒜,E(𝒜)) is said to have (ℬ,E(ℬ)) as a local hidden theory via L if for all states φ in E(𝒜), L*φ can be decomposed in E(ℬ) via a subcentral measure into states with pointwise strictly less dispersion than the dispersion of φ. After motivating this definition of local hidden theory it is shown that if, in addition, L factorizes on disjoint local algebras, then (ℬ, E(ℬ)) is not a local hidden theory of (𝒜,E(𝒜)) via L.
Geometric space-time perturbation. II. Gauge invariance
Authors: Maia M. D.
Published: July 2002

Using a multiparameter definition of space-time perturbation in a (4+n)-dimensional flat space, the question of identification gauge invariance of the background metric is examined. It is shown that when the allowed identification gauge transformations are given by rotations in the parameter space, then the background metric is invariant. A possible association with Kaluza–Klein theory is also examined.
Systematics of arbitrary-helicity Lagrangian wave equations
Authors: Collins Graham P. , Doughty Noel A.
Published: July 2002

The nontrivially gauge-invariant Lagrangian field equations of arbitrary helicity are constructed directly by integration of the corresponding non-Lagrangian Poincaré field strengths based on the Lorentz irreps of unmixed spin. All the details of the gauge properties of the Lagrangian formulation of the free massless Poincaré irrep fields are derived systematically and uniformly for arbitrary spin from the very simple field-strength formulation as a direct consequence of an integration process. The gauge transformations, including the tracelessness of the gauge parameters, the form of the fermionic and bosonic potential field equations (first-, and second-order, respectively), and the vanishing double trace of the higher-spin (≥ (7)/(2) ) potentials are all seen to be natural consequences of the integration of the classical equations for the field strengths without need for appeal to other requirements such as those of quantum field theory. Thus the equivalence (modulo gauge freedom and derivability from a Lagrangian) of the field strength and standard potential formulations of classical free fields are demonstrated explicitly, and uniformly for arbitrary helicity.
On the WKBJ approximation
Authors: El Sawi M.
Published: July 2002

A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form (SF) that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution.
The problem of moments in the phase-space formulation of quantum mechanics
Authors: Narcowich Francis J.
Published: July 2002

Long ago, Moyal [Proc. Cambridge Philos. Soc. 45, 99 (1949)] formulated a moment problem in the context of the Wigner–Weyl phase-space formulation of quantum mechanics. The problem amounts to giving necessary and sufficient conditions for a sequence of numbers to be moments of a Wigner function. In this paper, that problem is solved, and so is a truncated version of it.
The Riemann–Hilbert problem for the supersymmetric constraint equations
Authors: Tafel J.
Published: July 2002

Different formulations of the Riemann–Hilbert problem related to the constraint equations in supersymmetric Yang–Mills theories are discussed.
On a Painlevé test of a coupled system of Boussinesq and Schrödinger equations
Authors: Chanda Pranab K. , Chowdhury A. Roy
Published: July 2002

The complete integrability of a new system of nonlinear equations using the technique of Painlevé analysis has been investigated. The system essentially represents a coupling of Boussinesq and Schrödinger equations through nonlinear terms. While the arbitrariness of the expansion coefficients are proved (for a particular branch) in the formalism of Weiss et al. [J. Math. Phys. 24, 522 (1983)], with the reduced ansatz of Kruskal, the consistency of the truncation is proved by a combination of the methodology due to Weiss [J. Math. Phys. 25, 13, 2226 (1984)] and Hirota [Lecture Notes in Physics, Vol. 515 (Springer, Berlin, 1976)]. On the other hand, the Bäcklund transformation for the equations are obtained via the truncation procedure, without the use of Kruskal’s simplification.
Canonical transformations in quantum mechanics: A canonically invariant path integral
Authors: Shiekh A. Y.
Published: July 2002

A particular form of the path integral is presented that allows the implementation of general canonical transformations in quantum mechanics, as well as a consistent quantization procedure.
Finite moment equations for a relativistic simple gas
Authors: Majorana A.
Published: July 2002

This paper on the relativistic Boltzmann equation deals with the derivation of moment equations for a simple gas. It is shown that for a neutrino gas and for a hard-sphere model in the ultrarelativistic case, the moment equations at each order contain only a finite number of moments of the distribution function.
Integrable forms of the one-dimensional flow equation for unsaturated heterogeneous porous media
Authors: Broadbridge P.
Published: July 2002

The equation for the horizontal transport of a liquid in an unsaturated scale-heterogeneous porous medium is ∂θ/∂t=λ(x)∂/∂x[C(θ)∂θ/∂x] −λ′(x)E(θ)∂θ/∂x−λ″(x)∫(C+E)dθ. A systematic search for Lie–Bäcklund symmetries leads to the requirement that C=a(b−θ)−2, as in the homogeneous (λ=1) case. More generally, (λ,E) may be ((1+mx)α, (1/α− (3)/(2) )C) or (exp(mx),−3C/2). In these cases the transport equation may be linearized and solved exactly. Examples of more complicated heterogeneous extensions are presented for the integrable nonlinear diffusion equations and for Burgers’ equation.
Nonlocal symmetries and the linearization of the massless Thirring and the Federbush models
Authors: Kersten Paul H. M.
Published: July 2002

Multilation of nonlocal symmetries of the massless Thirring and the Federbush models leads to transformations linearizing these equations.
All possible local charges in a local quantum field theory: Massive case
Authors: Amigó J. M.
Published: July 2002

A proof for local charges of the classical result first put forward by Coleman and Mandula [Phys. Rev. 159, 1251 (1967)] is given. Local charges are operators defined as integrals of the time component of conserved Hermitian density currents; in interacting theories they happen to be generators of symmetries of the S matrix.
The matrix representations of g2. I. Representations in an so(4) basis
Authors: Le Blanc R. , Rowe D. J.
Published: July 2002

Irreducible representations of the real compact Lie algebra g2 are given in g2⊇so(4) bases. All missing labels are accounted for by the explicit construction of a g2⊇so(4) basis of vector holomorphic functions. The general problem of missing internal labels is also briefly discussed.
On biorthogonal and orthonormal Clebsch–Gordan coefficients of SU(3): Analytical and algebraic approaches
Authors: Ališauskas Sigitas
Published: July 2002

Minimal biorthogonal systems of the Clebsch–Gordan (Wigner) coefficients of SU(3)⊇U(2) are discussed as well as the dual coupled bases. The closed system of analytical expressions for the dual isofactors (reduced Wigner coefficients) and the overlaps of coupled states is obtained with the help of analytical inversion symmetry. The Regge-type symmetry of the overlaps and the boundary orthonormal isofactors (orthogonalization coefficients) is discovered. The polynomial structure of the alternative complete algebraic systems of the orthonormal SU(3) isofactors (characterized by the null spaces, symmetries, and additional selection rules and obtained by means of the Hecht or Gram–Schmidt process) is considered. The realizations of the external ‘‘missing label’’ operators of the third and the fourth orders in the minimal coupled bases, which lead to preferable algorithms to evaluate the orthonormal SU(3) coupling coefficients satisfying different symmetry properties, are presented. With the help of the 6j coefficients of SU(2) or inverted truncated SU(2) recoupling matrices, the biorthogonal systems associated with the SU(3) canonical tensor operators are expanded in terms of minimal ones.
Sensitive terms in the path integral: Ordering and stochastic options
Authors: Gaveau B. , Schulman L. S.
Published: July 2002

In a previous publication [Phys. Rev. D 36, 1135 (1987)] it was shown how the stochastic process associated with the solution of the Schrödinger or diffusion equation can be derived by an infinity of ‘‘Gaussian tricks.’’ In this article the method is extended to differential operators of the form (p−eA/c)2, ∂c2(x)∂, and Δ =(1/(g)1/2)∂μ((g)1/2gμν∂ν). In this formulation the relation between operator ordering ambiguities and time labeling in the functional integral is immediate. In particular, it is clear where the choice between Ito and Stratonovich integrals enters.
Dichotomies for linear periodic differential equations with impulses
Authors: Milev N. V. , Bainov D. D.
Published: July 2002

In the present paper the exponential and ordinary dichotomies for linear periodic differential equations with impulses are investigated.
A systematic approach to the soliton equations of a discrete eigenvalue problem
Authors: Schilling Randolph James
Published: July 2002

The Ablowitz–Ladik (AL) problem is a linear vector difference equation whose isospectral flow equations include several important soliton equations; e.g., the discrete nonlinear Schrödinger equation: iq̇n=qn−1−2qn+qn+1 +‖qn‖2(qn−1+qn+1). There is an established procedure for describing the soliton hierarchy of the more familiar AKNS (Ablowitz, Kaup, Newell and Segur)problem. It is based on the notion of a generator for the hierarchy. In this paper the soliton equations of the AL hierarchy are described and characterized by a generator pair. A new continuous spectral problem is introduced and the AKNS hierarchy is embedded in its hierarchy as a specialization.
Gupta–Bleuler quantization of free massless Lagrangian gauge fields of arbitrary helicity: The bosonic case
Authors: Doughty Noel A. , Arnold Richard A.
Published: July 2002

The Gupta–Bleuler canonical quantization procedure for free massless gauge fields is applied to the Lagrangian potentials of arbitrary integer helicity. The supplementary conditions required to limit the particle states to the physical subspace of positive-definite metric and positive energy are explicitly set out using procedures that are uniform for all spins, bosonic and fermionic. The well-known lower-spin results (spins 1 and 2), where some of the arbitrary spin features are vacuous, arise as special cases.
Foldy–Wouthuysen-type reduction of the second-order Dirac equation
Authors: Hostler Levere
Published: July 2002

A nonrelativistic reduction of the second-order Dirac equation is investigated. An equation K2+[Π0; K−Π̂]=m2+Π̂2 is obtained for a ‘‘kinetic Hamiltonian’’ K such that Φ obeys a nonrelativistic Schrödinger-type equation Π0Φ=KΦ in addition to obeying the second-order Dirac equation. Non-self-adjoint terms in K are removed by a change of representation from Φ to ΦT ≡PΦ, and a closed expression P≡[ 1/2 +(K† −Π̂)(K−Π̂)/2(m)2]1/2 is obtained for P. Similar results are obtained for antiparticle states, and a type of ‘‘factorization theorem’’ for the second-order Dirac equation is obtained in which the second-order Dirac equation is replaced by a pair of uncoupled first-order equations. Since nonperturbative techniques are used throughout, the factorization theorem holds independently of the question of convergence of the Foldy–Wouthuysen series and is valid whenever the equation K2+[Π0; K−Π̂]=m2+Π̂2 admits a solution for K. The connection with the usual linear Dirac equation is investigated, and closed expressions are described for a transformation to a representation of that equation which is ‘‘even’’ in the language of Foldy and Wouthuysen. The transformation described is equivalent to two consecutive ‘‘odd’’ unitary transformations.
Some remarks on Einstein–Maxwell solitons
Authors: Salazar I. Humberto
Published: July 2002

A short expression is given for the gravitational and electromagnetic potential of N Kerr–Newman particles. The free parameters of the solution and some limiting cases are discussed.
Dyons in affine field theories
Authors: Cadavid A. C. , Finkelstein R. J.
Published: July 2002

By postulating that the gauge vector field and the Higgs field both lie in an affine algebra rather than a Lie algebra, an affine field theory with an expanded soliton sector is obtained. An infinite family of exact, special solutions of the new equations corresponding to the original ’t Hooft–Polyakov solitonic solutions, is now found. A perturbation method for an arbitrary solution of the new equation is also proposed.
On some nonunitary representations of the Poincaré group and their use for the construction of free quantum fields
Authors: Cassinelli G. , Olivieri G. , Truini P. , Varadarajan V. S.
Published: July 2002

In this paper a class of nonunitary infinite dimensional Hilbert space representations of a semidirect product is investigated. The equivalence of this category with the category of finite dimensional representations of the stability subgroups is shown. This theory is applied to the Poincaré group and to the construction of free quantum fields. In an appendix a method is introduced for building an infinite family of finite dimensional indecomposable representations of the noncompact Euclidean group in two dimensions. Such representations are used for carrying out the analysis of the massless fields.
Radiative transfer theory for inhomogeneous media with random extinction and scattering coefficients
Authors: Manning Robert M.
Published: July 2002

The small-angle scattering approximation of the scalar radiative transfer equation is examined in the case where the extinction and scattering coefficients have a component that is a deterministic function of position along the propagation path and a component that is a random function of position transverse to the propagation direction. It is found that the resulting stochastic radiative transfer equation can be reduced to a system of two stochastic integrodifferential equations for the average and fluctuating components of the radiant intensity. The system is solved to yield two transfer equations: one that describes the average radiant intensity and one that describes the spatial correlation function of the intensity fluctuations. The integrodifferential equation for the average intensity is then solved and applied to a simple propagation scenario; it is found that the fluctuations in the extinction and scattering coefficients reduce the effects due to the average values of these parameters, and also that the effect of these is greater near the point of observation than near the point of transmission of the radiation. An approximate solution is also derived for the equation giving the correlation function. The equations developed here should find application in problems involving short wavelength electromagnetic wave propagation through media possessing variable characteristics of turbulence and turbidity, such as in plasmas, the atmosphere, and the ocean.
One more theorem on the short-time regeneration rate
Authors: Exner Pavel
Published: July 2002

Consider an unstable quantum system that has been found undecayed at an instant s and denote by R(t,s) the rate of its regeneration into an original (undecayed) state at a later instant t+s. It is proved that the reduced evolution is a semigroup, i.e., there is no regeneration at all, provided R(t,s)1/2 can be estimated by a sufficiently regular function that is nondecreasing in s and has zero derivative with respect to t at t=0 for every s. This generalizes the theorem of Misra and Sinha [Helv. Phys. Acta 45, 619 (1972)] in a different direction than in a recent paper by Nishioka [J. Math. Phys. 29, 1860 (1988)].
Distributions of ℏ-positive type and applications
Authors: Narcowich Francis J.
Published: July 2002

States in classical mechanics are probability measures, and their Fourier transforms are continuous functions of positive type. States in the phase-space formulation of quantum mechanics are Wigner distribution functions, and their (symplectic) Fourier transforms have been characterized by Kastler [Commun. Math. Phys. 1, 14 (1965)] and Loupias and Miracle-Sole [Commun. Math. Phys. 2, 31 (1966); Ann. Insto. H. Poincaré 6, 39 (1967)] as being continuous functions of ‘‘ℏ-positive type.’’ In this paper, (Schwartz) distributions of ℏ-positive type, are defined and studied. It is shown that if such distributions are bounded on a certain sequence of test functions, then they are symplectic Fourier transforms of Wigner distribution functions. These results, are applied to a variety of problems ranging from ones involving the quantum Liouville equation to a problem in signal analysis.
New similarity reductions of the Boussinesq equation
Authors: Clarkson Peter A. , Kruskal Martin D.
Published: July 2002

Some new similarity reductions of the Boussinesq equation, which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering, are presented. These new similarity reductions, including some new reductions to the first, second, and fourth Painlevé equations, cannot be obtained using the standard Lie group method for finding group-invariant solutions of partial differential equations; they are determined using a new and direct method that involves no group theoretical techniques.
Highest weight irreducible unitarizable representations of Lie algebras of infinite matrices. The algebra A∞
Authors: Palev Tchavdar D.
Published: July 2002

In this paper all unitarizable irreducible highest weight representations of the infinite-dimensional Lie algebra A∞, which is a completion and central extension of the general linear Lie algebra gl∞, are considered. Within each representation space a basis is introduced and expressions for the transformations of the basis under the action of the Chevalley generators are written.
Reduction, quantization, and nonunimodular groups
Authors: Tuynman G. M.
Published: July 2002

It is shown that even in relatively nice cases the naive approach to the quantization of constraints is not correct in general [i.e., the procedure that if f=0 is a classical constraint and τ(f) is the associated quantum operator, then the quantum constraint is τ(f)=0]. An explicit procedure for the quantization of constraints in the case of a configuration space with a symmetry group is provided and proven, where the reduced configuration space is the orbit space. It is not thought that the group acts freely, merely that all isotropy subgroups are conjugated to each other.
Algebras for the two-sphere and the three-sphere groups of compact simple Lie groups
Authors: Bose S. K. , Bruce S. A.
Published: July 2002

The infinite-dimensional Lie algebras corresponding to the Lie groups of smooth maps from two and three spheres to compact simple Lie groups are studied. The problem of their central extension is solved. The problem of the existence of semidirect sum algebras containing these and the algebras of the groups of diffeomorphisms on the two and three spheres is treated.
Schrödinger processes and large deviations
Authors: Dawson D. , Gorostiza L. , Wakolbinger A.
Published: July 2002

For a large system of independent diffusing particles, each of which is killed at a certain space-time dependent rate, the conditional distribution of surviving trajectories in a bounded time interval is computed, given the approximate form of the initial and final empirical distribution of surviving particles. This generalizes a result for the Brownian case without killing, which was first obtained by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. 1931, 144].