The Rotation Average in Lightcone Time-Ordered Perturbation Theory

We present a rotation average of the two-body scattering amplitude in the lightcone time($\tau$)-ordered perturbation theory. Using a rotation average procedure, we show that the contribution of individual time-ordered diagram can be quantified in a Lorentz invariant way. The number of time-ordered diagrams can also be reduced by half if the masses of two bodies are same. In the numerical example of $\phi^{3}$ theory, we find that the higher Fock-state contribution is quite small in the lightcone quantization.Comment: 25 pages, REVTeX, epsf.sty, 69 eps file

Analysis of ADCP data above a bottom observatory

A 300-kHz ADCP was set on GEOSTAR, a six-m3 deep-sea observatory. It was operated with cells of 80 cm during a three-week test experiment at 42-m water depth in the northern Adriatic sub-basin. Although it provided valuable data about the horizontal current field over most of the water column, it also allowed specifying the wake disturbances induced by the observatory. These disturbances are characterised by vertical velocities that are significant up to ~20 m above seafloor (echo intensity data suggest that the wake can even reach the surface), and by inclinations of the bottom nepheloïd layer (as deduced from differences in echo intensities from beam to beam). Our analysis is validated by consistent relationships between the horizontal current direction and speed on one side and the characteristics of both dynamical (vertical velocity) and non-dynamical (echo intensity) parameters on the other side. It is in good agreement with the simulations from a numerical model, and hence specifies the sensitivity (especially with respect to echo intensity) and accuracy of an instrument usually operated within fields of current and scatterers not disturbed by the device supporting it. In addition, the error velocity parameter displays specific characteristics that easily allow specifying the thickness of the layer disturbed by the observatory, thus providing a technique to validate the quality of data acquired in similar conditions

Relativistic three-particle scattering equations

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.Comment: 5pages, text and one ps figure (in revtex) include

Role of retardation in 3-D relativistic equations

Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of anti-particles, is identical to the use of time-ordered diagrams, and has been used within the framework of $\phi^2\sigma$ coupling to study the role of energy dependence and non-locality when the two-body potential is the sum of $\sigma$-exchange and crossed $\sigma$ exchange. The results show that non-locality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.Comment: 17 pages, RevTeX; 8 figures. Accepted for publication in Phys. Rev. C56 (Nov. 97

Relativistic Quantum Mechanics - Particle Production and Cluster Properties

This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a bounded number of bare-particle degrees of freedom. The focus of this paper is about the realization of cluster properties in these theories.Comment: 36 pages, Late

Two-fermion relativistic bound states in Light-Front Dynamics

In the Light-Front Dynamics, the wave function equations and their numerical solutions, for two fermion bound systems, are presented. Analytical expressions for the ladder one-boson exchange interaction kernels corresponding to scalar, pseudoscalar, pseudovector and vector exchanges are given. Different couplings are analyzed separately and each of them is found to exhibit special features. The results are compared with the non relativistic solutions.Comment: 40 pages, to be published in Phys. Rev. C, .tar.gz fil

Relativistic instant-form approach to the structure of two-body composite systems

A new approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main novel feature of this approach is the new method of construction of the matrix element of the electroweak current operator. The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of the electromagnetic current also the conservation law automatically. The properties of the system as well as the approximations are formulated in terms of form factors. The approach makes it possible to formulate relativistic impulse approximation in such a way that the Lorentz-covariance of the current is ensured. In the electromagnetic case the current conservation law is ensured, too. The results of the calculations are unambiguous: they do not depend on the choice of the coordinate frame and on the choice of "good" components of the current as it takes place in the standard form of light--front dynamics. Our approach gives good results for the pion electromagnetic form factor in the whole range of momentum transfers available for experiments at present time, as well as for lepton decay constant of pion.Comment: 26 pages, Revtex, 5 figure

Entanglement of Fock-space expansion and covariance in light-front Hamiltonian dynamics

We investigate in a model with scalar ``nucleons'' and mesons the contributions of higher Fock states that are neglected in the ladder approximation of the Lippmann-Schwinger equation. This leads to a breaking of covariance, both in light-front and in instant-form Hamiltonian dynamics. The lowest Fock sector neglected has two mesons in the intermediate state and corresponds to the stretched box. First we show in a simplified example that the contributions of higher Fock states are much smaller on the light-front than in instant-form dynamics. Then we show for a scattering amplitude above threshold that the stretched boxes are small, however, necessary to retain covariance. For an off energy-shell amplitude covariance is not necessarily maintained and this is confirmed by our calculations. Again, the stretched boxes are found to be small.Comment: 17 pages, revtex, 14 figures, submitted to Phys.Rev.

Light-Front Bethe-Salpeter Equation

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests that the convergence of the expansion is rapid. This result is particular for light-front dynamics. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional ones. The technical procedure is developed for a two-boson case; the idea for an extension to fermions is given. The technical procedure appears quite practicable, possibly allowing one to go beyond the ladder approximation for the solution of the Bethe-Salpeter equation. The relation between the three-dimensional light-front reduction of the field-theoretic Bethe-Salpeter equation and a corresponding quantum-mechanical description is discussed.Comment: 42 pages, 5 figure

Unitarity and the Bethe-Salpeter Equation

We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the $\phi^2\sigma$ interaction Lagrangian and the $\pi N$ system with $s$-, $u$-, and $t$-channel pole diagrams as driving terms. We observe that the equal-time equation, which includes some of the three-body unitarity cuts, gives the best agreement with the Bethe-Salpeter result. This is followed by other 3-D approximations that have less of the analytic structure.Comment: 17 pages, 8 figures; RevTeX. Version accepted for publication in Phys. Rev.