76 research outputs found
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
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
Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons
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. Here we begin important tests of the
relativistic sixteen component wave function solutions obtained in a recent
work on meson spectroscopy, extending a method developed previously for
positronium decay into two photons. Preliminary to this we examine the
positronium decay in the 3P_{0,2} states as well as the 1S_0. The two-gamma
quarkonium decays that we investigate are for the \eta_{c}, \eta_{c}^{\prime},
\chi_{c0}, \chi_{c2}, \pi^{0}, \pi_{2}, a_{2}, and f_{2}^{\prime} mesons. Our
results for the four charmonium states compare well with those from other quark
models and show the particular importance of including all components of the
wave function as well as strong and CM energy dependent potential effects on
the norm and amplitude. The results for the \pi^{0}, although off the
experimental rate by 15%, is much closer than the usual expectations from a
potential model. We conclude that the Two-Body Dirac equations lead to wave
functions which provide good descriptions of the two-gamma decay amplitude and
can be used with some confidence for other purposes.Comment: 79 pages, included new sections on covariant scalar product and added
pages on positronium decay for 3P0 and 3P_2 state
Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics
Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics
have been successfully applied to obtain a covariant nonperturbative
description of QED and QCD bound states. Coulomb-type potentials in these
applications lead naively in other approaches to singular relativistic
corrections at short distances that require the introduction of either
perturbative treatments or smoothing parameters. We examine the corresponding
singular structures in the effective potentials of the relativistic
Schroedinger equation obtained from the Pauli reduction of the TBDE. We find
that the relativistic Schroedinger equation lead in fact to well-behaved wave
function solutions when the full potential and couplings of the system are
taken into account. The most unusual case is the coupled triplet system with
S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the
effective S-state potential would become attractively singular. We show how
including the tensor coupling is essential in order that the wave functions be
well-behaved at short distances. For example, the S-state wave function becomes
simply proportional to the D-state wave function and dips sharply to zero at
the origin, unlike the usual S-state wave functions. Furthermore, this behavior
is similar in both QED and QCD, independent of the asymptotic freedom behavior
of the assumed QCD vector potential. Light- and heavy-quark meson states can be
described well by using a simplified linear-plus-Coulomb-type QCD potential
apportioned appropriately between world scalar and vector potentials. We use
this potential to exhibit explicitly the origin of the large pi-rho splitting
and effective chiral symmetry breaking. The TBDE formalism developed here may
be used to study quarkonia in quark-gluon plasma environments.Comment: 23 pages, 4 figure
Is the Regge Calculus a consistent approximation to General Relativity?
We will ask the question of whether or not the Regge calculus (and two
related simplicial formulations) is a consistent approximation to General
Relativity. Our criteria will be based on the behaviour of residual errors in
the discrete equations when evaluated on solutions of the Einstein equations.
We will show that for generic simplicial lattices the residual errors can not
be used to distinguish metrics which are solutions of Einstein's equations from
those that are not. We will conclude that either the Regge calculus is an
inconsistent approximation to General Relativity or that it is incorrect to use
residual errors in the discrete equations as a criteria to judge the discrete
equations.Comment: 27 pages, plain TeX, very belated update to match journal articl
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