English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this second paper we complete the classical description of an isolatedsystem of "charged positive-energy particles, with Grassmann-valued electriccharges and mutual Coulomb interaction, plus a transverse electro-magneticfield" in the rest-frame instant form of dynamics.  In particular we show how to determine a collective variable associated withthe internal 3-center of mass on the instantaneous 3-spaces, to be eliminatedwith the constraints ${\vec {\cal K}}_{(int)} \approx 0$. Here ${\vec {\calK}}_{(int)}$ is the Lorentz boost generator in the unfaithful internalrealization of the Poincare' group and its vanishing is the gauge fixing to therest-frame conditions ${\vec {\cal P}}_{(int)} \approx 0$. We show how to findthis collective variable for the following isolated systems: a) chargedparticles with a Coulomb plus Darwin mutual interaction; b) transverseradiation field; c) charged particles with a mutual Coulomb interaction plus atransverse electro-magnetic field.  Then we define the Dixon multipolar expansion for the open particlesubsystem. We also define the relativistic electric dipole approximation ofatomic physics in the rest-frame instant form and we find the a possiblerelativistic generalization of the electric dipole representation.

canadian journal of physics

Towards Relativistic Atomic Physics. II. Collective and Relative  Relativistic Variables for a System of Charged Particles plus the  Electro-Magnetic Field