Theory of Nucleon-Nucleon Scattering

We present a new study of kinematical problems of relativistic nucleon-nucleon interactions, more complete than the previous studies. Two-component spinor formalism is used throughout. Several choices of spinor bases, their relations, crossing relations in all channels, helicity amplitudes, partial-wave amplitudes, the absence of kinematical singularities, and unitarity are discussed. The contributions of arbitrary intermediate states J in the unitarity are summed and the Regge forms for all five scalar amplitudes are obtained.     

Construction of Covariant Bases for Two-Particle Reactions

A method for the construction of the Lorentz-covariant bases occurring in the decomposition of spinor amplitudes (M-functions) of four massive particle processes is given. Each particle of spin- is described by a spinor state of the type-(s, 0) and/or (0, s), but the essential parts of our method apply whatever the type of spinor state used, and the necessary relations between the hitherto familiar types of spinor states are given, by means of which the relationship between the resulting sets of invariant amplitudes can be made explicit. By way of illustration four worked examples are presented.     

Maximum likelihood estimation of structural wave components from noisy data

In this paper, a general framework is developed for determining the underlying parameters of general signal models through the application of maximum likelihood estimation theory for functions whose variables separate. This method extends previous work in sinusoidal and exponential estimation to include models with other functional bases, such as exponential functions with nonconstant amplitudes and Bessel functions. Nonuniform spatial sampling is also possible with this technique. The maximum likelihood method is applied to the identification of wave components along one-dimensional structural elements. Results are given which demonstrate the viability and accuracy of the technique estimating exponential and Bessel function model parameters from noisy simulation data.     

The Holomorphic Quadratic Differentials of Amplitudes for Strings with Boundaries

We show that the amplitudes for strings with boundaries can be written as complex structure forms. The C, curves used by Krichever and Novikov to parametrize compact Riemann surfaces satisfy the string boundary conditions. Thus they can be regarded as the initial and final states of the atrings. Using Krichever-Novikov bases, we explicitly construct a basis of holomorphic quadratic differentials for strings with boundaries.     

Calculation of multiloop amplitudes in the theory of closed oriented superstrings

Multiloop superstring amplitudes are obtained upon integrating local amplitudes with respect to modular parameters of the Schottky supergroup and with respect to vertex coordinates in the nonsplit (1|1) complex supermanifold. Ambiguities in this integration are removed by the condition requiring that the local symmetries of the amplitudes under discussion be conserved. Local superstring amplitudes are calculated by summing local fermion-string amplitudes. The resulting superstring amplitudes are free from divergencies. The vacuum amplitude is zero, in just the same way as the one-, two-, and three-point massless-boson amplitudes are. The amplitudes in question vanish after integration of corresponding local amplitudes with respect to interaction-vertex coordinates and with respect to the limiting points of the Schottky supergroup, with the exception of those (3|2) points that are fixed by SL(2) symmetry.     

Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system(HTGS)is established by introducing frequency disturbance in this paper.Based on the proposed model,the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams,time waveforms and phase portraits.We find that stability and operational characteristics of the HTGS change with the value of system parameter k_d.Furthermore,the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out.Meanwhile,we obtain that the relative deviation of the mechanical torque mt rises with the increase of a.These methods and results of the study,combined with the performance of two time scales and the fast-slow coupled engineering model,provide some theoretical bases for investigating interesting physical phenomena of the engineering system.     

Asymptotic method for determining the amplitude for three-particle breakup: Neutron-deuteron scattering

The process of neutron-deuteron scattering at energies above the deuteron-breakup threshold is described within the three-body formalism of Faddeev equations. Use is made of the method of solving Faddeev equations in configuration space on the basis of expanding wave-function components in the asymptotic region in bases of eigenfunctions of specially chosen operators. Asymptotically, wave-function components are represented in the form of an expansion in an orthonormalized basis of functions depending on the hyperangle. This basis makes it possible to orthogonalize the contributions of elastic-scattering and breakup channels. The proposed method permits determining scattering and breakup parameters from the asymptotic representation of the wave function without reconstructing it over the entire configuration space. The scattering and breakup amplitudes for states of total spin S = 1/2 and 3/2 were obtained for the s-wave Faddeev equation.     

倾斜井眼中感应测井正演模拟与响应特征

感应测井仪器的发射源可简化为一系列磁偶极子,其在层状地层中产生的电磁场可分解成彼此独立的TE波和TM波叠加,且TE波和TM波完全由两个标量方程确定.首先研究倾斜井眼中磁偶极子场的TE波和TM波分解,推导多层介质中电磁场振幅以及地层界面上广义反射和透射系数的递推公式,给出层状地层电磁场解析解.然后利用数值结果分析考察砂泥岩薄交互层中,地层层厚、井眼倾角变化等对感应测井响应的影响.     

Complete and effectively complete inclusive experiments

The experiments required to meadure all the independent amplitudes in any single-particle inclusive process with experimentally available incident particles are determined, and the amplitude (or combination of amplitudes) obtained from each measurement is given. Various kinematic regions are considered, and the measurements which determine the subset of amplitudes expected to be important in each region are found. The prospects of a meaningful separation of exchanged naturalities are also investigated and found to be difficult, due to a kinematic suppression of certain amplitudes.     

Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm

In papers [Jafarizadehn and Salimi, Ann. Phys. 322, 1005 (2007) and J. Phys. A: Math. Gen. 39, 13295 (2006)], the amplitudes of continuous-time quantum walk (CTQW) on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated with their adjacency matrix. Here in this paper, it is shown that the CTQW on any arbitrary graph can be investigated by spectral analysis method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition (GQD) have been introduced, where this is achieved simply by relaxing some of the constrains imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit vectors of strata are identical with the orthonormal basis produced by Lanczos algorithm. Moreover, it is shown that probability amplitude of observing the walk at a given vertex is proportional to its coefficient in the corresponding unit vector of its stratum, and it can be written in terms of the amplitude of its stratum. The capability of Lanczos-based algorithm for evaluation of CTQW on graphs (GQD or non-QD types), has been tested by calculating the probability amplitudes of quantum walk on some interesting finite (infinite) graph of GQD type and finite (infinite) path graph of non-GQD type, where the asymptotic behavior of the probability amplitudes at the limit of the large number of vertices, are in agreement with those of central limit theorem of [Phys. Rev. E 72, 026113 (2005)]. At the end, some applications of the method such as implementation of quantum search algorithms, calculating the resistance between two nodes in regular networks and applications in solid state and condensed matter physics, have been discussed, where in all of them, the Lanczos algorithm, reduces the Hilbert space to some smaller subspaces and the problem is investigated in the subspace with maximal dimension.     

Off-mass shell dual amplitudes (II)

A new method for continuing dual model amplitudes off the mass shell was recently proposed. This paper explores some of the properties of the resulting amplitudes. It is demonstrated that one-current amplitudes contain fixed poles in the J-plane at positions that are correlated with the asymptotic power behavior of form factors. The two-point function is explicitly calculated and shown to fall asymptotically as a power provided that a certain condition involving the dimension of space-time and a parameter (that is believed to be correlated with the leading Regge intercept) is satisfied. Certain formulas required for future investigation of more complicated amplitudes are also derived.     

On the uniqueness of the smooth zero mass limit for invariant amplitudes

The behavior of the invariant amplitudes for processes involving massive vector mesons is investigated in the limit as the mass goes to zero. The constraints of gauge invariance impose a definite structure on the amplitudes at k² = 0, and the question of the uniqueness of this structure is examined. It is shown that if the limit is smooth, the consequent relations between the massive and massless helicity amplitudes are unique, provided only that any additional dynamical assumptions are made consistently. Some of the implications of this result are discussed, with particular reference to the unambiguous covariant formulation of vector meson dominance for scattering amplitudes.     

Decay amplitudes and resonances

The structure of a type of decay amplitudes, which we considered recently and its connection to scattering amplitudes (of arbitrary arrangement channel cases), to conventional decay amplitudes, and to the energy distribution is worked out in detail. The meaning of unperturbed energies in usual approaches is clarified. Our considerations include the case of overlapping resonances. Sum rules for transition amplitudes, such as are of interest for neutral kaon decays, are rigorously derived. The exact interrelations between various approaches are shown.     

Recursion relations and scattering amplitudes in the light-front formalism

The fragmentation functions and scattering amplitudes are investigated in the framework of light-front perturbation theory. It is demonstrated that, the factorization property of the fragmentation functions implies the recursion relations for the off-shell scattering amplitudes which are light-front analogs of the Berends–Giele relations. These recursion relations on the light-front can be solved exactly by induction and it is shown that the expressions for the off-shell light-front amplitudes are represented as a linear combinations of the on-shell amplitudes. By putting external particles on-shell we recover the scattering amplitudes previously derived in the literature.     

Non-archimedean string dynamics

Explicit formulas for the N-point tree amplitudes of the non-archimedean open string are derived. These amplitudes can be generated from a simple non-local lagrangian involving a single scalar field (the tachyon) in ambient space-time. This lagrangian is studied and is found to possess a tachyon free vacuum with no “particles” but with soliton solutions. The question of generalizing the adelic product formular to N-point amplitudes is taken up. The infinite product of 5-point amplitudes is shown to converge in a suitably chosen kinematic region whence it can be analytically continued. Though the precise form of the product formula for the 5-point (and N-point)amplitudes is not found, it is shown that the product is not equal to one as it is for the 4-point amplitudes but rather involves the famous zeros of the Riemann zeta function. Chan-Paton rules for non-archimedean open strings are given. A string over the (global) field of rational numbers is constructed. Other problems that are addressed are the introduction of supersymmetry, the nature of a p-adic string lagrangian, and the possibility of strings over other locally compact fields.     

Renormalization in the complete Mellin representation of Feynman amplitudes

The Feynman amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM integrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched.     

On the analytic properties of the reggeon-reggeon amplitude

The analytic properties of the reggeon-reggeon amplitude in the missing-mass like variable are discussed. (This amplitude is defined through the suitable high-energy limit of the eight-point amplitude). It is shown on the basis of simple Feynman diagrams that it is possible to define reduced amplitudes which are free from kinematical singularities provided that the eight-point amplitude is expressed in a form explicitly consistent with Steinmann relations. In a simple model which is considered in this paper, the reduced amplitudes have the singularity structure of ordinary two-body scattering amplitudes. The finite energy sum rules and four reggeon vertices are also briefly discussed.     

Quark-gluon amplitudes in the dual expansion

The dual representation, which gives a simple analytical form for purely gluonic amplitudes, is extended to amplitudes which include a quark-antiquark pair. To minimize the calculations, supersymmetry is used to relate the purely gluonic amplitudes to those including a gluino pair from which the quark-antiquark amplitudes are easily deduced. We explicitly give simple analytical forms for the full amplitudes for those multi-parton processes which involve a quark-antiquark pair plus two, three and four gluons.     

PartiallyU(1) compactified scalar massless field on the compact Riemann surface and the bosonic string amplitudes

The theory of the partiallyU(1) compactified scalar massless field on the compact Riemann surface with Nambu-Goto action is defined. The partition function is determined completely by a choice of the finite-dimensional approximations. The correlation functions are the only correctly defined objects of the theory. The averages of the correlation function asymptotic values provide the amplitudes. For the compact Riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes.     

Improvement of Multichannel Amplitudes for the Pion-Pion Scattering Using the Dispersion Relations

The multichannel S- and P-wave amplitudes for the ππ scattering, constructed requiring analyticity and unitarity of the S-matrix and using the uniformization procedure, are elaborated using the dispersion relations with imposed crossing symmetry condition. The amplitudes are modified in the low-energy region to improve their consistency with experimental data and the dispersion relations. Agreement with data is achieved for both amplitudes from the threshold up to 1.8 GeV and with dispersion relations up to 1.1 GeV. Consequences of the applied modifications, e.g. changes of the S-wave lowest-pole positions, are presented.