748 research outputs found
The Lorentz-Dirac and Landau-Lifshitz equations from the perspective of modern renormalization theory
This paper uses elementary techniques drawn from renormalization theory to
derive the Lorentz-Dirac equation for the relativistic classical electron from
the Maxwell-Lorentz equations for a classical charged particle coupled to the
electromagnetic field. I show that the resulting effective theory, valid for
electron motions that change over distances large compared to the classical
electron radius, reduces naturally to the Landau-Lifshitz equation. No
familiarity with renormalization or quantum field theory is assumed
Helicity supersymmetry of dyons
The 'dyon' system of D'Hoker and Vinet consisting of a spin 1/2 particle with
anomalous gyromagnetic ratio 4 in the combined field of a Dirac monopole plus a
Coulomb plus a suitable potential (which arises in the long-range limit
of a self-dual monopole) is studied following Biedenharn's approach to the
Dirac-Coulomb problem: the explicit solution is obtained using the
`Biedenharn-Temple operator', , and the extra two-fold degeneracy is
explained by the subtle supersymmetry generated by the 'Dyon Helicity' or
generalized `Biedenharn-Johnson-Lippmann' operator . The new SUSY
anticommutes with the chiral SUSY discussed previously.Comment: 14 pages, 2 figure
Unified description of 0+ states in a large class of nuclear collective models
A remarkably simple regularity in the energies of 0+ states in a broad class
of collective models is discussed. A single formula for all 0+ states in
flat-bottomed infinite potentials that depends only on the number of dimensions
and a simpler expression applicable to all three IBA symmetries in the large
boson number limit are presented. Finally, a connection between the energy
expression for 0+ states given by the X(5) model and the predictions of the IBA
near the critical point is explored.Comment: 4 pages, 3 postscript figures, uses revTe
Critical sets of the total variance of state detect all SLOCC entanglement classes
We present a general algorithm for finding all classes of pure multiparticle
states equivalent under Stochastic Local Operations and Classsical
Communication (SLOCC). We parametrize all SLOCC classes by the critical sets of
the total variance function. Our method works for arbitrary systems of
distinguishable and indistinguishable particles. We also discuss the Morse
indices of critical points which have the interpretation of the number of
independent non-local perturbations increasing the variance and hence
entanglement of a state. We illustrate our method by two examples.Comment: 4 page
Operator Transformations Between Exactly Solvable Potentials and Their Lie Group Generators
One may obtain, using operator transformations, algebraic relations between
the Fourier transforms of the causal propagators of different exactly solvable
potentials. These relations are derived for the shape invariant potentials.
Also, potentials related by real transformation functions are shown to have the
same spectrum generating algebra with Hermitian generators related by this
operator transformation.Comment: 13 pages with one Postscript figure, uses LaTeX2e with revte
The Vector Analyzing Power in Elastic Electron-Proton Scattering
We compute the vector analyzing power (VAP) for the elastic scattering of
transversely polarized electrons from protons at low energies using an
effective theory of electrons, protons, and photons. We study all contributions
through second order in , where and are the electron energy and
nucleon mass, respectively. The leading order VAP arises from the imaginary
part of the interference of one- and two-photon exchange amplitudes.
Sub-leading contributions are generated by the nucleon magnetic moment and
charge radius as well as recoil corrections to the leading-order amplitude.
Working to , we obtain a prediction for that is free of
unknown parameters and that agrees with the recent measurement of the VAP in
backward angle scattering.Comment: 24 pages, 11 figures. Typos fixe
Kinematics and hydrodynamics of spinning particles
In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.Comment: LaTeX file; needs kapproc.st
Advanced action in classical electrodynamics
The time evolution of a charged point particle is governed by a second-order
integro-differential equation that exhibits advanced effects, in which the
particle responds to an external force before the force is applied. In this
paper we give a simple physical argument that clarifies the origin and physical
meaning of these advanced effects, and we compare ordinary electrodynamics with
a toy model of electrodynamics in which advanced effects do not occur.Comment: 12 pages, 5 figure
Exact Evolution Operator on Non-compact Group Manifolds
Free quantal motion on group manifolds is considered. The Hamiltonian is
given by the Laplace -- Beltrami operator on the group manifold, and the
purpose is to get the (Feynman's) evolution kernel. The spectral expansion,
which produced a series of the representation characters for the evolution
kernel in the compact case, does not exist for non-compact group, where the
spectrum is not bounded. In this work real analytical groups are investigated,
some of which are of interest for physics. An integral representation for the
evolution operator is obtained in terms of the Green function, i.e. the
solution to the Helmholz equation on the group manifold. The alternative series
expressions for the evolution operator are reconstructed from the same integral
representation, the spectral expansion (when exists) and the sum over classical
paths. For non-compact groups, the latter can be interpreted as the (exact)
semi-classical approximation, like in the compact case. The explicit form of
the evolution operator is obtained for a number of non-compact groups.Comment: 32 pages, 5 postscript figures, LaTe
Potential Scattering in Dirac Field Theory
We develop the potential scattering of a spinor within the context of
perturbation field theory. As an application, we reproduce, up to second order
in the potential, the diffusion results for a potential barrier of quantum
mechanics. An immediate consequence is a simple generalization to arbitrary
potential forms, a feature not possible in quantum mechanics.Comment: 7 page
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