527 research outputs found
Causal Classical Theory of Radiation Damping
It is shown how initial conditions can be appropriately defined for the
integration of Lorentz-Dirac equations of motion. The integration is performed
\QTR{it}{forward} in time. The theory is applied to the case of the motion of
an electron in an intense laser pulse, relevant to nonlinear Compton
scattering.Comment: 8 pages, 2 figure
Helical Symmetry in Linear Systems
We investigate properties of solutions of the scalar wave equation and
Maxwell's equations on Minkowski space with helical symmetry. Existence of
local and global solutions with this symmetry is demonstrated with and without
sources. The asymptotic properties of the solutions are analyzed. We show that
the Newman--Penrose retarded and advanced scalars exhibit specific symmetries
and generalized peeling properties.Comment: 11 page
Order reductions of Lorentz-Dirac-like equations
We discuss the phenomenon of preacceleration in the light of a method of
successive approximations used to construct the physical order reduction of a
large class of singular equations. A simple but illustrative physical example
is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure
Late-Time Behavior of Stellar Collapse and Explosions: I. Linearized Perturbations
Problem with the figures should be corrected. Apparently a broken uuencoder
was the cause.Comment: 16pp, RevTex, 6 figures (included), NSF-ITP-93-8
Regulator constants and the parity conjecture
The p-parity conjecture for twists of elliptic curves relates multiplicities
of Artin representations in p-infinity Selmer groups to root numbers. In this
paper we prove this conjecture for a class of such twists. For example, if E/Q
is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p
extension, then the p-parity conjecture holds for twists of E by all orthogonal
Artin representations of Gal(K^\infty/Q). We also give analogous results when
K/Q is non-abelian, the base field is not Q and E is replaced by an abelian
variety. The heart of the paper is a study of relations between permutation
representations of finite groups, their "regulator constants", and
compatibility between local root numbers and local Tamagawa numbers of abelian
varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat
Singularity-Free Electrodynamics for Point Charges and Dipoles: Classical Model for Electron Self-Energy and Spin
It is shown how point charges and point dipoles with finite self-energies can
be accomodated into classical electrodynamics. The key idea is the introduction
of constitutive relations for the electromagnetic vacuum, which actually
mirrors the physical reality of vacuum polarization. Our results reduce to
conventional electrodynamics for scales large compared to the classical
electron radius cm. A classical simulation for a
structureless electron is proposed, with the appropriate values of mass, spin
and magnetic moment.Comment: 3 page
Radiation from a charged particle and radiation reaction -- revisited
We study the electromagnetic fields of an arbitrarily moving charged particle
and the radiation reaction on the charged particle using a novel approach. We
first show that the fields of an arbitrarily moving charged particle in an
inertial frame can be related in a simple manner to the fields of a uniformly
accelerated charged particle in its rest frame. Since the latter field is
static and easily obtainable, it is possible to derive the fields of an
arbitrarily moving charged particle by a coordinate transformation. More
importantly, this formalism allows us to calculate the self-force on a charged
particle in a remarkably simple manner. We show that the original expression
for this force, obtained by Dirac, can be rederived with much less computation
and in an intuitively simple manner using our formalism.Comment: Submitted to Physical Review
On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg
In previous paper derivations of the Green function have been given for 5D
off-shell electrodynamics in the framework of the manifestly covariant
relativistic dynamics of Stueckelberg (with invariant evolution parameter
). In this paper, we reconcile these derivations resulting in different
explicit forms, and relate our results to the conventional fundamental
solutions of linear 5D wave equations published in the mathematical literature.
We give physical arguments for the choice of the Green function retarded in the
fifth variable .Comment: 16 pages, 1 figur
Aspects of electrostatics in a weak gravitational field
Several features of electrostatics of point charged particles in a weak,
homogeneous, gravitational field are discussed using the Rindler metric to
model the gravitational field. Some previously known results are obtained by
simpler and more transparent procedures and are interpreted in an intuitive
manner. Specifically: (i) We show that the electrostatic potential of a charge
at rest in the Rindler frame is expressible as A_0=(q/l) where l is the affine
parameter distance along the null geodesic from the charge to the field point.
(ii) We obtain the sum of the electrostatic forces exerted by one charge on
another in the Rindler frame and discuss its interpretation. (iii) We show how
a purely electrostatic term in the Rindler frame appears as a radiation term in
the inertial frame. (In part, this arises because charges at rest in a weak
gravitational field possess additional weight due to their electrostatic
energy. This weight is proportional to the acceleration and falls inversely
with distance -- which are the usual characteristics of a radiation field.)
(iv) We also interpret the origin of the radiation reaction term by extending
our approach to include a slowly varying acceleration. Many of these results
might have possible extensions for the case of electrostatics in an arbitrary
static geometry. [Abridged Abstract]Comment: 26 pages; accepted for publication in Gen.Rel.Gra
The canonical structure of Podolsky's generalized electrodynamics on the Null-Plane
In this work we will develop the canonical structure of Podolsky's
generalized electrodynamics on the null-plane. This theory has second-order
derivatives in the Lagrangian function and requires a closer study for the
definition of the momenta and canonical Hamiltonian of the system. On the
null-plane the field equations also demand a different analysis of the
initial-boundary value problem and proper conditions must be chosen on the
null-planes. We will show that the constraint structure, based on Dirac
formalism, presents a set of second-class constraints, which are exclusive of
the analysis on the null-plane, and an expected set of first-class constraints
that are generators of a U(1) group of gauge transformations. An inspection on
the field equations will lead us to the generalized radiation gauge on the
null-plane, and Dirac Brackets will be introduced considering the problem of
uniqueness of these brackets under the chosen initial-boundary condition of the
theory
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