175 research outputs found

### Centre-of-mass and internal symmetries in classical relativistic systems

The internal symmetry of composite relativistic systems is discussed. It is
demonstrated that Lorentz-Poincar\'e symmetry implies the existence of internal
moments associated with the Lorentz boost, which are Laplace-Runge-Lenz (LRL)
vectors. The LRL symmetry is thus found to be the internal symmetry universally
associated with the global Lorentz transformations, in much the same way as
internal spatial rotations are associated with global spatial rotations. Two
applications are included, for an interacting 2-body system and for an
interaction-free many-body system of particles. The issue of localizability of
the relativistic CM coordinate is also discussed

### General classical theory of spinning particles in a maxwell field

The purpose of this paper is to give the complete classical theory of a spinning particle moving in a Maxwell field. The particle is assumed to be a point, and its interaction with the field is described by a point charge g1 and a point dipole g2. The Maxwell equations are assumed to hold right up to the point representing the particle. Exact equations are then derived for the motion of the particle in a given external field which are strictly consistent with the conservation of energy, momentum and angular momentum, and hence contain the effects of radiation reaction on the motion of the particle. It is shown that in the presence of a point dipole the energy tensor of the field can and must be redefined so as to make the total energy finite. The mass, the angular momentum of the spin, and the moment of inertia perpendicular to the spin axis appear in the equations as arbitrary mechanical constants. Reasons are given for believing that for an elementary particle the last constant is zero, in agreement with relativistic quantum theory. In the general theory there is no relation between the electric and magnetic dipole moments of the particle and the state of its translational motion. A procedure is given for deriving from the general equations specialized equations consistent with the condition that the dipole is always a purely magnetic or electric one in the system in which the particle is instantaneously at rest. The radiation reaction terms are very much simpler in the former of these specialized cases than in the general case. The effect of radiation reaction is to make the scattering of light by a rotating dipole decrease inversely as the square of the frequency for high frequencies, just as for scattering by a point charge

### Iterative Approach to Gravitational Lensing Theory

We develop an iterative approach to gravitational lensing theory based on
approximate solutions of the null geodesic equations. The approach can be
employed in any space-time which is ``close'' to a space-time in which the null
geodesic equations can be completely integrated, such as Minkowski space-time,
Robertson-Walker cosmologies, or Schwarzschild-Kerr geometries. To illustrate
the method, we construct the iterative gravitational lens equations and time of
arrival equation for a single Schwarzschild lens. This example motivates a
discussion of the relationship between the iterative approach, the standard
thin lens formulation, and an exact formulation of gravitational lensing.Comment: 27 pages, 2 figures, submitted to Phys.Rev.D, minor revisions, new
reference

### Dynamics of test bodies with spin in de Sitter spacetime

We study the motion of spinning test bodies in the de Sitter spacetime of
constant positive curvature. With the help of the 10 Killing vectors, we derive
the 4-momentum and the tensor of spin explicitly in terms of the spacetime
coordinates. However, in order to find the actual trajectories, one needs to
impose the so-called supplementary condition. We discuss the dynamics of
spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.Comment: 11 pages, RevTex forma

### Quantization of Nonstandard Hamiltonian Systems

The quantization of classical theories that admit more than one Hamiltonian
description is considered. This is done from a geometrical viewpoint, both at
the quantization level (geometric quantization) and at the level of the
dynamics of the quantum theory. A spin-1/2 system is taken as an example in
which all the steps can be completed. It is shown that the geometry of the
quantum theory imposes restrictions on the physically allowed nonstandard
quantum theories.Comment: Revtex file, 23 pages, no figure

### Twistors, special relativity, conformal symmetry and minimal coupling - a review

An approach to special relativistic dynamics using the language of spinors
and twistors is presented. Exploiting the natural conformally invariant
symplectic structure of the twistor space, a model is constructed which
describes a relativistic massive, spinning and charged particle, minimally
coupled to an external electro-magnetic field. On the two-twistor phase space
the relativistic Hamiltonian dynamics is generated by a Poincare scalar
function obtained from the classical limit (appropriately defined by us) of the
second order, to an external electro-magnetic field minimally coupled, Dirac
operator. In the so defined relativistic classical limit there are no Grassman
variables. Besides, the arising equation that describes dynamics of the
relativistic spin differs significantly from the so called Thomas Bergman
Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything
else in the papper) on page 23 delete

### Generalized Euler Angle Paramterization for SU(N)

In a previous paper (math-ph/0202002) an Euler angle parameterization for
SU(4) was given. Here we present the derivation of a generalized Euler angle
parameterization for SU(N). The formula for the calculation of the Haar measure
for SU(N) as well as its relation to Marinov's volume formula for SU(N) will
also be derived. As an example of this parameterization's usefulness, the
density matrix parameterization and invariant volume element for a
qubit/qutrit, three qubit and two three-state systems, also known as two qutrit
systems, will also be given.Comment: 36 pages, no figures; added qubit/qutrit work, corrected minor
definition problems and clarified Haar measure derivation. To be published in
J. Phys. A: Math. and Ge

### Mathisson's helical motions for a spinning particle --- are they unphysical?

It has been asserted in the literature that Mathisson's helical motions are
unphysical, with the argument that their radius can be arbitrarily large. We
revisit Mathisson's helical motions of a free spinning particle, and observe
that such statement is unfounded. Their radius is finite and confined to the
disk of centroids. We argue that the helical motions are perfectly valid and
physically equivalent descriptions of the motion of a spinning body, the
difference between them being the choice of the representative point of the
particle, thus a gauge choice. We discuss the kinematical explanation of these
motions, and we dynamically interpret them through the concept of hidden
momentum. We also show that, contrary to previous claims, the frequency of the
helical motions coincides, even in the relativistic limit, with the
zitterbewegung frequency of the Dirac equation for the electron

### Spacetime dynamics of spinning particles - exact electromagnetic analogies

We compare the rigorous equations describing the motion of spinning test
particles in gravitational and electromagnetic fields, and show that if the
Mathisson-Pirani spin condition holds then exact gravito-electromagnetic
analogies emerge. These analogies provide a familiar formalism to treat
gravitational problems, as well as a means for comparing the two interactions.
Fundamental differences are manifest in the symmetries and time projections of
the electromagnetic and gravitational tidal tensors. The physical consequences
of the symmetries of the tidal tensors are explored comparing the following
analogous setups: magnetic dipoles in the field of non-spinning/spinning
charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter
spacetimes. The implications of the time projections of the tidal tensors are
illustrated by the work done on the particle in various frames; in particular,
a reciprocity is found to exist: in a frame comoving with the particle, the
electromagnetic (but not the gravitational) field does work on it, causing a
variation of its proper mass; conversely, for "static observers," a stationary
gravitomagnetic (but not a magnetic) field does work on the particle, and the
associated potential energy is seen to embody the Hawking-Wald spin-spin
interaction energy. The issue of hidden momentum, and its counterintuitive
dynamical implications, is also analyzed. Finally, a number of issues regarding
the electromagnetic interaction and the physical meaning of Dixon's equations
are clarified.Comment: 32+11 pages, 5 figures. Edited and further improved version, with new
Section C.2 unveiling analogies for arbitrary spin conditions, and new Sec.
3.2.3 in the Supplement making connection to the post-Newtonian
approximation; former Sec. III.B.4 and Appendix C moved to the (reshuffled)
Supplement; references updated. The Supplement is provided in ancillary file.
Matches the final published versio

### Stokes Parameters as a Minkowskian Four-vector

It is noted that the Jones-matrix formalism for polarization optics is a
six-parameter two-by-two representation of the Lorentz group. It is shown that
the four independent Stokes parameters form a Minkowskian four-vector, just
like the energy-momentum four-vector in special relativity. The optical filters
are represented by four-by-four Lorentz-transformation matrices. This
four-by-four formalism can deal with partial coherence described by the Stokes
parameters. A four-by-four matrix formulation is given for decoherence effects
on the Stokes parameters, and a possible experiment is proposed. It is shown
also that this Lorentz-group formalism leads to optical filters with a symmetry
property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.

- â€¦