287 research outputs found
The Rotation Average in Lightcone Time-Ordered Perturbation Theory
We present a rotation average of the two-body scattering amplitude in the
lightcone time()-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 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 coupling to study the
role of energy dependence and non-locality when the two-body potential is the
sum of -exchange and crossed 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
interaction Lagrangian and the system with -, -,
and -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.
- …