33 research outputs found
Non-Inertial Frames in Minkowski Space-Time, Accelerated either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics
After a review of the existing theory of non-inertial frames and mathematical
observers in Minkowski space-time we give the explicit expression of a family
of such frames obtained from the inertial ones by means of point-dependent
Lorentz transformations as suggested by the locality principle. These
non-inertial frames have non-Euclidean 3-spaces and contain the differentially
rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to
replace mathematical accelerated observers with dynamical ones (their
world-lines belong to interacting particles in an isolated system) and of how
to define Unruh-DeWitt detectors without using mathematical Rindler uniformly
accelerated observers. Also some comments are done on the transition from
relativistic classical mechanics to relativistic quantum mechanics in
non-inertial frames
Two gamma quarkonium and positronium decays with Two-Body Dirac equations of constraint dynamics
Two-Body Dirac equations of constraint dynamics provide a covariant framework
to investigate the problem of highly relativistic quarks in meson bound states.
This formalism eliminates automatically the problems of relative time and
energy, leading to a covariant three dimensional formalism with the same number
of degrees of freedom as appears in the corresponding nonrelativistic problem.
It provides bound state wave equations with the simplicity of the
nonrelativistic Schroedinger equation. Unlike other three-dimensional
truncations of the Bethe-Salpeter equation, this covariant formalism has been
thoroughly tested in nonperturbatives contexts in QED, QCD, and nucleon-nucleon
scattering. Here we continue the important studies of this formalism by
extending a method developed earlier for positronium decay into two photons to
tests on the sixteen component quarkonium wave function solutions obtained in
meson spectroscopy. We examine positronium decay and then the two-gamma
quarkonium decays of eta_c, eta'_c, chi_0c, chi_2c, and pi-zero The results for
the pi-zero, although off the experimental rate by 13%, is much closer than the
usual expectations from a potential model.Comment: 4 pages. Presented at Second Meeting of APS Topical Group on Hadron
Physics, Nashville, TN, Oct 22-24. Proceedings to be published by Journal of
Physics (UK), Conference Serie
Relativistic Generalization of the Post-Prior Equivalence for Reaction of Composite Particles
In the non-relativistic description of the reaction of composite particles,
the reaction matrix is independent of the choice of post or prior forms for the
interaction. We generalize this post-prior equivalence to the relativistic
reaction of composite particles by using Dirac's constraint dynamics to
describe the bound states and the reaction process.Comment: 3 pages in LaTex. Invited talk presented at the Third Joint Meeting
of Chinese Physicists Worldwide in Hong Kong, 2000, to be published in the
proceeding
Applications of Two Body Dirac Equations to Hadron and Positronium Spectroscopy
We review recent applications of the Two Body Dirac equations of constraint
dynamics to meson spectroscopy and describe new extensions to three-body
problems in their use in the study of baryon spectroscopy. We outline unique
aspects of these equations for QED bound states that distinguish them among the
various other approaches to the relativistic two body problem. Finally we
discuss recent theorectial solutions of new peculiar bound states for
positronium arising from the Two Body Dirac equations of constraint dynamics,
assuming point particles for the electron and the positron.Comment: Invited talk: CST-MISC joint international symposium on particle
physics - From spacetime dynamics to phenomenology - Tokyo, March 15-16, 201
Meson-Meson Scattering in Relativistic Constraint Dynamics
Dirac's relativistic constraint dynamics have been successfully applied to
obtain a covariant nonperturbative description of QED and QCD bound states. We
use this formalism to describe a microscopic theory of meson-meson scattering
as a relativistic generalization of the nonrelativistic quark-interchange model
developed by Barnes and Swanson.Comment: 5 pages, 1 figure in LaTex, talk present at the First Meeting of the
APS Topical Group on Hadronic Physics (Fermilab, October 24-26, 2004
Singularity-Free Breit Equation from Constraint Two-Body Dirac Equations
We examine the relation between two approaches to the quantum relativistic
two-body problem: (1) the Breit equation, and (2) the two-body Dirac equations
derived from constraint dynamics. The Breit equation is known to be
pathological when singularities appear at finite separations in the reduced
set of coupled equations for attractive potentials even when the potentials
themselves are not singular there. They then give rise to unphysical bound
states and resonances. In contrast, the two-body Dirac equations of constraint
dynamics do not have these pathologies in many nonperturbative treatments. To
understand these marked differences, we first express these contraint equations
in a hyperbolic form. These coupled equations are then re-cast into two
equivalent equations: (1) a covariant Breit-like equation with potentials that
are exponential functions of certain ``generator'' functions, and (2) a
covariant orthogonality constraint on the relative momentum. This reduction
enables us to show in a transparent way that finite- singularities do not
appear as long as the the exponential structure is not tampered with and the
exponential generators of the interaction are themselves nonsingular for finite
. These Dirac or Breit equations, free of the structural singularities which
plague the usual Breit equation, can then be used safely under all
circumstances, encompassing numerous applications in the fields of particle,
nuclear, and atomic physics which involve highly relativistic and strong
binding configurations.Comment: 38 pages (REVTeX), (in press in International Journal of Modern
Physics