General formalism in collinear regime for pseudoscalar meson production in NN collisions

The spin structure of the matrix element for the pseudoscalar meson production processes in nucleon-nucleon collisions is established in the collinear kinematical regime in terms of 3 independent scalar amplitudes. This result is valid for any reaction mechanism and for any energy of the colliding and the produced particles. The complete experiment for the full reconstruction of all 3 complex amplitudes must contain two different classes of polarization experiments. The polarization transfer coefficients can be used to determine the moduli of all 3 amplitudes, whereas the spin correlation coefficients for + collisions are sensitive to the relative phases of different amplitudes. Received: 13 August 2001 / Accepted: 20 September 2001     

符号关系式在测定含重原子晶体结构中的应用——Ⅰ.一个符号修正方案

对于由序数相近的原子所构成的晶体,Sayre等式给出了衍射结构振幅之间的关系。在测定由碳、氮、氧等“轻”原子构成的中心对称晶体结构中,利用Sayrs等式曾获得不少结果。但是对于含“重原子’的晶体,Sayre等式即不再适用。此时通常都利用所谓“重原子法”来解结构。本文讨论了含重原子情况下,晶体的结构振幅符号、Sayre符号,以及重原子符号之间的关系,从而指出了将重原子法和Sayre法结合的可能性,并提出了一个结构振幅符号的循环修正方案,借此有可能从重原子符号或一套包含若干错误的结构振幅符号出发,不经过电子密度综合而最终获得正确的结构振幅符合。将此方法试用于一个假想的一维晶体结构,效果良好。本文还讨论了有关在实际的晶体结构测定中应用的若干问题。     

Singularities of Adelic Feynman Amplitudes

We study adelic ⁴-theory with propagator, given by homogeneous adelic function. It is shown that almost all ultraviolet and infrared poles of Euclidean Feynman amplitude are cancelled by zeroes of the infinite product of p-adic Feynman amplitudes. Analytic continuation in the degree of homogeneity of general adelic Feynman amplitude is constructed. We prove that all adelic ⁴-theory amplitudes can be continued to the half-plane. There are an infinite number of amplitudes whose natural domain of analyticity is given by this half-plane provided the Riemann conjecture about -function zeroes is valid.     

Sound-wave coherence in atmospheric turbulence with intrinsic and global intermittency

The coherence function of sound waves propagating through an intermittently turbulent atmosphere is calculated theoretically. Intermittency mechanisms due to both the turbulent energy cascade (intrinsic intermittency) and spatially uneven production (global intermittency) are modeled using ensembles of quasiwavelets (QWs), which are analogous to turbulent eddies. The intrinsic intermittency is associated with decreasing spatial density (packing fraction) of the QWs with decreasing size. Global intermittency is introduced by allowing the local strength of the turbulence, as manifested by the amplitudes of the QWs, to vary in space according to superimposed Markov processes. The resulting turbulence spectrum is then used to evaluate the coherence function of a plane sound wave undergoing line-of-sight propagation. Predictions are made by a general simulation method and by an analytical derivation valid in the limit of Gaussian fluctuations in signal phase. It is shown that the average coherence function increases as a result of both intrinsic and global intermittency. When global intermittency is very strong, signal phase fluctuations become highly non-Gaussian and the average coherence is dominated by episodes with weak turbulence.     

Symmetry and some consequences for spin-particle reactions

On the basis of general spacetime and crossing symmetry, the general structure for amplitudes describing spin-particle binary reactions is considered. Using the knowledge of the kinematic structure of helicity amplitudes in the dynamical amplitude approach, we can get as model-independent general consequences about observable quantities, as some asymptotic relations between polarization parameters on the basis of a “kinematic hierarchy” assumption.     

The inclusion of fermions in dual N-point functions

Dual amplitudes of the five-point function for two fermions and three scalar bosons are constructed, and are used to obtain a consistent procedure for inclusing two fermions in the general N-point function.     

Zur elektronischen Struktur ungeordneter eindimensionaler Systeme. II. Verlauf der Streuparameter als Funktion der Energie

Statements on the energy dependence of the three scattering parameters are made for general energy dependent and non-local potentials used in a preceding paper [1] in a one-dimensional model for the electronic structure of disordered systems. All results are also valid in the relativistic case. The possible types for the behaviour of the wave function within the gaps and the form of the scattering parameters for δ-potentials are discussed.     

Renormalization of Feynman amplitudes and parametric integral representation

A new substraction formula is presented to renormalize Feynman amplitudes written in Schwinger's integral representation. The substractions are generated by an operator acting on the integrand, which only depends on the total number of internal lines but is completely independent of the structure of the graph. This formulation is also valid for non-renormalizable theories and is shown to reduce to Zimmermann'sR-operation for scalar theories. It satisfies in any case Bogoliubov's recursive formula and yields an explicit tool for actual computations of renormalized Feynman amplitudes with a minimal number of substractions.     

Universal boundary reflection amplitudes

For all affine Toda field theories we propose a new type of generic boundary bootstrap equations, which can be viewed as a very specific combination of elementary boundary bootstrap equations. These equations allow to construct general solutions for the boundary reflection amplitudes, which are valid for theories related to all simple Lie algebras, that is simply laced and non-simply laced. We provide a detailed study of these solutions for concrete Lie algebras in various representations. The boundary bootstrap equations relating different types of exited boundary states are not automatically solved by our expressions.     

Scattering of low-energy atoms by metallic surfaces

The problem of a neutral low-energy atom impinging on a well-defined metallic surface is approached from first principles. The solid and its potential energy of interaction with the incident atom is treated in the most general way, but under the following assumptions: (a) the conduction electrons interact adiabatically with the lattice ions and the gas atom; (b) no chemical reactions occur; (c) the one-phonon approximation is valid. The scattering amplitudes for surface and bulk mode excitations are obtained in terms of the dynamical properties of the metallic surface. Direct collisions of the incident atoms with the lattice ions are shown to give a negligible contribution to the scattering. The most important contribution comes from the interaction of the gas atom with the surface conduction electrons; the excitation of lattice vibrational modes occurs through the electron-phonon term of the Hamiltonian. The general expressions for the scattering amplitudes obtained show that the scattering is incoherent. With further assumptions one obtains a separation of the scattering amplitude into a coherent and incoherent part.     

Reciprocity in the wave reflection and transmission problem: Part 1. Symmetry of the matrices of reflection coefficients

The reciprocity theorem in Lyamshev’s formulation is used to derive a general symmetry relationship for the matrices of reflection coefficients in homogeneous media and one-dimensional waveguides. This relationship is shown to be equivalent to the normalization of the amplitudes by the cross power flux of the forward and backward waves. The relationship is valid for both propagating and evanescent waves, and all the symmetry relationships known from the literature represent its particular cases.     

On the equations of state in quantum statistical mechanics

By extending methods previously used to study the equations of state at low temperature, it is shown that the entropy density and the statistical average of a conserved, non-spontaneously violated, charge density can be expanded in terms of integrals over products of many body n-point amplitudes defined for real, continuous frequencies. The general structure of the expansions is described, and it is demonstrated that essentially the same spectral function determines the entropy density and the average charge densities. Certain classes of terms are worked out in detail, and the formal sum of one such class is shown to provide the contributions to the equations of state arising from composite quasiparticles associated with the poles of the n-point amplitudes. [Another term, discussed in many previous works, involves the logarithms of the elementary propagators and yields the contributions to the equations of state coming from elementary quasiparticles.]The Appendices include an extensive study of the analytic properties of many body amplitudes in the frequencies of the external and internal lines. Specialized to zero temperature, these considerations apply to the Feynman diagrams for elementary particle amplitudes.     

The helicity amplitude approach to low energy theorems

It is shown that “low energy theorems” for charged vector and axial vector currents have a natural derivation in terms of helicity amplitudes. This is done by reconsidering the kinematic constraints as a function of the virtual photon mass, λ. The crucial point is that in general a certain limit of the longitudinal amplitudes is required as an input to the theorem. Two new νπ sum rules are also obtained.     

Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31–45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.     

Reciprocal space-time and momentum-space singularities in the narrow resonance approximation

A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonnace approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x² (x^μ being a position vector). This scheme is made precise by dual string off-shell amplitudes. As well as highlighting possible connections between the general dual framework and the structure of confined field theories we are able to pinpoint certain grave shortcomings of present dual models.     

Inversion of atom diffraction intensities for surface structural determination

Atom diffraction from surfaces has proved to be a very useful method for structural studies on surfaces, particularly for incommensurate layers and hydrogen adlayers which are not easily analyzed with LEED. We have developed a rapid method to obtain the surface corrugation function directly from the measured intensities within the hard wall model. This avoids a tedious search in parameter space to determine surface structures and is valid for surfaces whose corrugation amplitudes are below the Rayleigh limit. We will discuss the method and its sensitivity to experimental errors in determining the diffraction intensities as well as its applicability when only a fraction of the allowed diffraction beams are experimentally accessible.     

The Fourier-Bessel expansion of the scattering amplitude at zero momentum transfer for particles with unequal mass

We investigate the problem of whether a Fourier-Bessel type expansion can be valid at zero-momentum transfer for the unequal-mass scattering amplitude, as a substitute for the Regge-Watson-Sommerfeld representation. It is shown that the results of a previous paper, giving the solution of the same problem for amplitudes satisfying an unsubtracted dispersion relation can be extended to a class of asymptotically growing scattering amplitudes. In the second part of the paper a Lorentz-pole expansion is outlined, which is valid at arbitrary momentum transfer. The expansion coefficients of this last expansion are expressed by means of the discontinuities of the amplitudes. Finally, a comparison is made between the Fourier-Bessel expansion and the Lorentz expansion. We argue that, at least as far as the unequal-mass formulas are concerned, it is highly unnatural to assume that a pomeron with intercept α(0) = 1 belongs purely to the four-vector representation of the Lorentz group. Rather, it is a mixed object belonging to the four-dimensional and the accompanying infinite-dimensional ones, both characterized by the same Casimir operator eigenvalues.     

Covariant string amplitudes on exotic topologies to one loop

Rules are provided for the calculation of string amplitudes on all exotic topologies to one loop. These topologies include the real projective plane, the disk, the annulus, the Möbius strip, the torus and the Klein bottle. The rules are valid for bosonic strings, superstrings, and heterotic strings either in their critical dimensions or toroidally compactified, and they are applicable to amplitudes with arbitrary external bosonic and fermionic states, including mixed open- and closed-string transitions. The modular invariance of the torus amplitudes is discussed.     

Dissolving N = 4 loop amplitudes into QCD tree amplitudes

We use the infrared consistency of one-loop amplitudes in N = 4 Yang-Mills theory to derive a compact analytic formula for a tree-level next-to-next-to-maximal helicity-violating gluon scattering amplitude in QCD, the first such formula known. We argue that the infrared conditions, coupled with recent advances in calculating one-loop box coefficients, can give a new tool for computing tree-level amplitudes in general. Our calculation suggests that many amplitudes have a structure which is even simpler than that revealed so far by current twistor-space constructions.     

Current Algebra on the Torus

We derive the N-point one-loop correlation functions for the currents of an arbitrary affine Kac-Moody algebra. The one-loop amplitudes, which are elliptic functions defined on the torus Riemann surface, are specified by group invariant tensors and certain constant tau-dependent functions. We compute the elliptic functions via a generating function, and explicitly construct the invariant tensor functions recursively in terms of Young tableaux. The lowest tensors are related to the character formula of the representation of the affine algebra. These general current algebra loop amplitudes provide a building block for open twistor string theory, among other applications.