On the structure of the conformal covariant N-point functions

The conformal covariant n-point functions for the fields with arbitrary spin and scale dimension are found. These functions are determined up to a set of arbitrary functions on $\text{n(n?3)}\text{2}$ independent conformal invariant variables. These arbitrary functions cannot be determined without dynamical assumptions.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

Reggeon quantum mechanics: A critical discussion

The quantum-mechanical problem of reggeon field theory in zero transverse dimensions is re-examined in order to set up a precise mathematical framework for the case μ = α(0) ? 1 > 0. We establish a Hamiltonian formulation in a Hilbert space for (ifμ > 0) and we prove the equivalence of the related eigenvalue problem with a “radial” Schrödinger-type equation in an L²(0, ∞) space. We prove that the S-matrix and the pomeron Green functions, at fixed rapidity Y and triple-pomeron coupling λ ≠ 0, have a spectral decomposition and are analytic in μ for ?∞ < μ < + ∞. For μ > 0, we confirm most of the qualitative results found by previous authors, and in particular the tunnelling shift [～ exp(?μ²/2λ²)] setting the scale for the asymptotic behaviour in Y.In the classical limit of λ/μ small we find that the action, for μ > 0, develops a singularity in Y at some value Y_c. We give arguments to show that for Y ? Y_c the perturbative result is reached, while for $\text{Y ? Y}{}_{\mathrm{<mtext>c</mtext>}}$ perturbation theory breaks down. Most of these results are shown to be stable against the addition of a small quartic coupling of the simplest type [$\text{λ′(}\text{Ψ}\text{Ψ)}{}^2$] up to the “magic” vvalue λ′ = λ²/μ. The existence of a level crossing at this value is confirmed by an analytic continuation in λ′.     

Topological cross sections in hadron-nucleon and hadron-nucleus collisions at very high energies

We apply our microscopic model for the topological cross section σ_n to produce n charged particles in hadron-proton interactions to hadron-nucleus scattering. The model is based on a stochastic branching process for hadronization. We calculate multiplicity distributions of hadron-nucleus collisions for 50 GeV ? E_L ? 400 GeV based on a multiple collision model. The production of “grey” $\text{(0.3 <}\text{ν}\text{c}\text{< 0.7)}$ particles is considered together with the shower $\text{(}\text{ν}\text{c}\text{> 0.7)}$ particles in order to test the model for higher number of collisions. The joint probability distribution of numbers of shower and grey particles F(n_s, n_g) is calculated. Finally, we critically compare the results to experimental data.     

Energy loss mechanisms in low energy electron scattering from W(100) and their use as a surface sensitive spectroscopy

The energy loss spectrum of low energy (0 < E_p < 200 eV) electrons scattered from W(100) has been experimentally investigated, and mechanisms giving rise to the fine structure analyzed using a dielectric response formalism. The dielectric medium is characterized by available optical data and energy band calculations for tungsten. All of the structure for loss energies, w, less than 18 eV is attributed to intra- and interband transitions involving the bulk valence and conduction bands. The surface and bulk plasmon excitations are observed at w = 21 eV and w = 25.5 eV respectively which is in reasonable agreement with the optical data. A very narrow peak in the density of conduction d-band states apparently functions strongly in well defined excitations involving the $\text{5p}\text{3}\text{2}$ and 4f tungsten orbitais and the 2s and 2p orbitais of adsorbed oxygen. These conduction band states form a “window” with which to measure the electronic orbital structure of both the substrate and adsorbate during adsorption and reaction. We demonstrate this for the room temperature adsorption of oxygen on W(100) in which we observe the sequential filling of two electronically inequivalent binding states. The stability of the “d-band window” during thermally activated reaction, and the likelihood of its existence in other transition metals makes this an attractive surface sensitive spectroscopy.     

The supergroup manifold formulation of the Wess-Zumino multiplet revisited: The supercurrent and the supergravity auxiliary fields

In this paper we provide a consistent first-order group-manifold formulation of the Wess-Zumino system. It is shownhow the well-known auxiliary fields of the ($\text{1}\text{2}$, 0, 0) system arise by supplementing Bianchi identities with the “second-order constraints”; that is, those equations allowing the transition from the first order to the second order of the theory. When the ($\text{1}\text{2}$, 0, 0) multiplet is coupled to N = 1 supergravity and the torsion “second-order constraint” is implemented, we get a non-minimal set of auxiliary fields (scalar, pseudoscalar axial vector and a spinor). We argue this to be the fundamental set of auxiliary fields. The so-called “minimal set” is not coordinate invariant and can be recovered only by adding a non-geometrical constraint.     

Quantizing a classically ergodic system: Sinai's billiard and the KKR method

Sinai's “billiards on a torus,” i.e., free motion of a particle in a plane amongst reflecting discs of radius R centred on points of the unit square lattice, is a classically ergodic system with two freedoms, parametrized by R. Quantal energy levels E_n are given by the vanishing of the Korringa-Kohn-Rostoker (KKR) determinant of solid state theory. This gives a rapid computational scheme for computing E_n as functions of R. Except for the integrable case R = 0, no degeneracies are found, illustrating the theorem that two parameters, not one, are required to make levels cross in a generic system. The same theorem leads to the prediction that the probability distribution of the spacings S of neighbouring levels is $\text{O}$(S) as S → 0, in good agreement with computation. The KKR determinant is transformed analytically to give the level density d(E) semiclassically (i.e., as ? → 0) as the sum of a steady contribution $\text{d}\text{?}\text{(E)}$ and an oscillatory contribution d_osc(E). $\text{d}\text{?}$ is $\text{O}$(?^?2) and is given by the Weyl “area” formula plus “edge,” “corner” and “curvature” corrections, in excellent agreement with computation. d_osc is given by a sum over classical closed orbits (all unstable). Nonisolated closed orbits (not hitting discs) contribute terms with $\text{O}$$\text{(?}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext><mtext>)</mtext>}}$ to d_osc, while isolated closed orbits (bouncing between discs) contribute terms with $\text{O}$(?^?1) to d_osc. The isolated orbits are vastly more numerous than the nonisolated orbits and their contributions cannot be neglected. As a means of calculating the individual E_n (rather than the smoothed spectrum), the KKR method is much more efficient than the classical path sum.     

On the geometrical aspects of electromagnetism,I

The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′_μ. The nonlinearity is traded in for the correct characteristic $\text{e}\text{m}$ of the test particle through a gauge condition, imposed upon A′_μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the $\text{e}\text{m}$ ratio inside the gauge leaves F′_μν independent of $\text{e}\text{m}$ and allows its identification with the E.-M. tensor F_μν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the $\text{e}\text{m}$ ratio.     

Magnetic ordering in uranium monophosphide

The magnetic ordering in uranium monophosphide (UP) has been studied by neutron diffraction from a single crystal in a magnetic field. UP orders at T_N ? 122 ± 0.1 K with the type-I antiferromagnetic structure (+-+-), the ordering taking place in a first-order transition. At T₀ = 22.5 K the ordered magnetic moment jumps from 1.7 μ_B to 1.9 μ_B. With a magnetic field H = 25 kOe applied along the [11&#x0304;10] direction, it is found that UP has the collinear single-$\text{K}$ type-I structure above T₀ and undergoes a first-order transition to the planar double-$\text{K}$ type-I structure, accompanied by a “moment jump” due to the change in the moment direction from <001> to <110>.     

Electrical conductivity and defect structure of Ni-doped and “CO-reduced” Ni-doped SrTiO3 single crystals

The electrical conductivities of Ni-doped and “CO-reduced” Ni-doped SrTiO₃ single crystals were measured at temperatures 700–1200°C and P_o2's of 10^?7–10^?1 atm. Plots of log σ vs $\text{1}\text{T}$ at constant P_o2's were found to be linear, and the activation energies appeared to be 0.92 eV for Ni-doped SrTiO₃ and 0.50 eV for “CO-reduced” Ni-doped SrTiO₃ single crystals, respectively. Plots of log σ vs log P_o2 at constant temperature were found to be linear with an average slope of ?$\text{1}\text{4}$ for SrTiO₃:Ni and of ?$\text{1}\text{6}$ for “CO-reduced” SrTiO₃:Ni single crystals, respectively. The electrical conductivity dependencies on P_o2 indicate that a triply ionized titanium interstitial and an oxygen vacancy model are applicable to Nidoped and “CO-reduced” Ni-doped SrTiO₃ single crystals, respectively. The small polaron conduction was suggested on “CO-reduced” Ni-doped SrTiO₃ single crystal from the temperature dependence of conductivity.     

A possible constructive approach to (super-φ3)4 (III). On the normalization of Schwinger functions

The question of normalizability of (super-φ³)₄ is reduced to the verification of two conjectures pertaining to the construction of the infinite volume limit in the presence of a UV cutoff k. Assuming their validity it is shown that the image of the renormalization map covers a set at least as large as $\text{R}$₊³ for any k < ∞.     

Constraints on conformal invariant QED

Previous constraints on the parameters of a conformal invariant model of quantum electrodynamics are reviewed and extended. It is shown that the Schwinger-Dyson equation for the electron propagator is solved by the conformal covariant ansatz for the vertex function. This yields additional constraints on the model. One of these implies that at least one of the coefficients of the leading terms in the C = ?1, J = 1 part of the Wilson expansion for the product $\text{ψ(x)}\text{ψ}\text{(y)}$ of electron fields must have an esential singularity in the coupling constant if Z₃ is finite.     

Supersymmetry and the division algebras

We show how spinors in space-times of dimension D = t + s, where t is the time dimension, are associated for s - t = 1, 2, 4, 8 (and if t = 0, 1, 2) with the number systems (division algebras), $\text{|R, C, H, O}$. For t = 1 and s - t = 1, 2, 4 this association is “realized” by the sequence of Lorentz groups S1(2,$\text{|R}$), S1(2;$\text{|C}$), S1(2;$\text{|H}$) for D = 3, 4, 6 respectively. We discuss how octonions may be related to D = 10. For D = 6 we give details of S1(2; $\text{|H}$) spinors and construct supersymmetric models with them. These results explain various “empirical” observations in the literature relating quaternions and supersymmetry.     

Pseudoscalar mesons in the c-c and b-b systems

It is shown that the pseudoscalar η_c and “η_c” (η_b and “η_b”) with M ≈ 2.80 and 3.51 GeV (9.17 and 9.88 GeV) can be predicted by using the radial mixing model, where the “η_c” and “η_b” are the excited 0^- states in the $\text{c-}\text{c}$ and $\text{b-}\text{b}$ systems, respectively, and the former would correspond to the observed 0^- meson with M ≈ 3.45 GeV in charmonium.     

Associated production of heavy Higgs boson with top quarks

Associated production of a heavy Higgs boson (m_H > 100 GeV) with top quarks at Juratron energies is studied. It is natural to differentiate between the “light” (2m_t < m_H < 2m_W) and “heavy” (m_H > 2m_W) Higgs search. It is assumed that the mass value of the top quarks is in the interval m_t ≈ 30–80 GeV. m_W is the W-boson mass. If m_H < 2m_W a dangerous background is given by the QCD production of four top quarks. We have calculated the cross sections for both the Higgs production and the background reaction. The disappointing result found is that the background is overwhelmingly large. However the Higgs search in this mass region is not hopeless. The associated production of the Higgs boson with a W-boson may have a clear experimental signature, its background given by the reaction $\text{p}\text{+}\text{p}\text{→}\text{W}\text{+}\text{t}\text{+}\text{t}$ might be suppressed. The difficulty with this mechanism is that the rate is rather low. If m_H > 2m_W the background is different and its contribution is expected to be small. The associated production of a Higgs boson with a pair of top quarks might be a useful method in the Higgs search in this case.     

A positive energy dynamics and scattering theory for directly interacting relativistic particles

Starting from the tensor product of N irreducible positive energy representations of the Poincaré group describing N free relativistic particles with arbitrary spins and positive masses, we construct an interacting positive energy representation by modifying the total 4-momentum operator. We first make a transformation to a Hilbert space on which the free total 4-momentum operator equals the product of a dimensionless center-of-mass 4-vector ($\text{(|k|}{}^2\text{+ 1)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, k) and a free “reduced Hamiltonian” H_r⁰, which is a positive operator acting only on internal variables, and then replace H_r⁰ by an interacting reduced Hamiltonian H_r = H_r⁰ + V, where V commutes with the Lorentz group and is such that H_r is a positive operator. The resulting product form is shown to imply that the wave operators interwine the free and interacting representations so that the S-operator is Lorentz invariant. From a physical point of view the scheme is related to the framework first introduced by Bakamjian and Thomas, in which the Hamiltonian and boost generators are modified, but the above procedure makes a mathematically rigorous discussion much simpler. In the spin-zero case we introduce a natural generalization of the pair potentials of nonrelativistic N-particle Schrödinger theory to the present relativistic setting, study its scattering theory, and point out some problems that do not have analogs at the nonrelativistic level. In the $\text{spin}\text{-}\text{1}\text{2}$ case we propose, inspired by the Dirac equation, explicit reduced Hamiltonians to describe atomic energy levels and present arguments making plausible that their eigenvalues are in closer agreement with the experimental data than their nonrelativistic counterparts. We also consider extensions to arbitrary spin and, in the $\text{spin}\text{-}\text{1}\text{2}$ case, coupling of a quantized radiation field. In view of eventual applications to “completely integrable” one-dimensional field theories the case of one space dimension is studied as well, both in quantum mechanics and in classical mechanics.     

Analysis of the methods proposed for computing the scattering of atoms from a hard corrugated surface model of He/LiF (001)

It appears that the scattering of atoms on crystal surfaces is accounted for by a corrugated infinite wall model of the surface. To determine the “corrugation function” which represents best the experimental scattering intensities, it is necessary to choose among many possible versions, the simplest and most effective computational method of the theoretical scattering amplitudes. It is the purpose of this paper to analyze the relative merits of three particular versions which we call HDM, NHM and GR, and which are described in section 3. This comparison is carried out on the He/LiF(001) system for variable incident wave vector (k) and orientation (θ_i) as well as a number of Fourier components (ζ_G) used to describe the “corrugation function”. We conclude that the GR method presents advantages over the other two: (i) it reduces the computer time necessary for the HDM and NHM methods, (ii) converges and computes to within 10^?4 in unitarity the scattering amplitudes in a larger range of energies as well as angular and corrugation parameters, and (iii) it presents a great simplicity and the corrugation is very handy. The size of that range depends on the computer facilities used. In our case, the GR method works for any calculation in which kC₀ < 9 and $\text{C}{}_0\text{< 0.35}\text{A}\text{?}$ (where k is the incident wave vector and C₀ twice the amplitude of the corrugation). These characteristics prove to make the GR method a good tool for the study of surface crystallography by parametrization of the surface corrugation.