TY - CHAP

T1 - The relativistic action at a distance two body problem

AU - Horwitz, Lawrence P.

N1 - Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Associate legendre function

KW - Casimir operator

KW - Lorentz group

KW - Magnetic quantum number

KW - Principal series

UR - http://www.scopus.com/inward/record.url?scp=85091430068&partnerID=8YFLogxK

U2 - 10.1007/978-94-017-7261-7_5

DO - 10.1007/978-94-017-7261-7_5

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AN - SCOPUS:85091430068

T3 - Fundamental Theories of Physics

SP - 71

EP - 96

BT - Fundamental Theories of Physics

PB - Springer Science and Business Media Deutschland GmbH

ER -