The relativistic action at a distance two body problem

Lawrence P. Horwitz*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Models with action at a distance potentials, such as the Coulomb potential, have been very useful in nonrelativistic mechanics. They provide a simpler framework than the perhaps more fundamental field mediated models for interaction, and are also straightforwardly amenable to rigorous mathematical analysis. In this Newtonian-Galilean view, all events directly interacting dynamically occur simultaneously; the dynamical phase space of N particles contains the points xn(t) and pn(t), for n=1,2,3,...N; these points move through the phase space as a function of the parameter t, following some prescribed equations of motion. Two particles may be thought of as interacting through a potential function V(x1(t), x2(t)); for Galiliean invariance, V may be a scalar function of the difference, i.e., V(x1(t) − x2(t)). It is usually understood that x1 and x2 are taken to be at equal time, corresponding to a correlation between the two particles consistent with the Newtonian-Galilean picture. With the advent of special relativity, it became a challenge to formulate dynamical problems on the same level as that of the nonrelativistic theory.

Original languageEnglish
Title of host publicationFundamental Theories of Physics
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages26
StatePublished - 2015

Publication series

NameFundamental Theories of Physics
ISSN (Print)0168-1222
ISSN (Electronic)2365-6425


  • Associate legendre function
  • Casimir operator
  • Lorentz group
  • Magnetic quantum number
  • Principal series


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