Approximately Relativistic Lagrangians for Classical Interacting Point Particles. 3.
Apr, 197819 pages
Published in:
- Phys.Rev.D 17 (1978) 1985-2003
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Abstract: (APS)
In part I of this series the general form to order c−2 of approximately relativistic Lagrangians following from classical Poincaré-invariant variational principles of the Fokker type was established for point particles with two-body (neutral) interactons. In this paper the relativistic action principles discussed in I are generalized to include interactions involving classical isospin and the general form to order c−2 of the associated approximate Lagrangians is obtained by the methods developed in I. The post-Newtonian interaction may contain up to six independent functions of the interparticle separation and of the isospin vectors of each particle, in addition to the Newtonian potential. Unlike the neutral interactions considered in I, nonsymmetry of the particles' variables in the relativistic interaction can be evident in order c−1 as well as c−2. The form of the ten conservation laws following from Poincaré invariance and of the charge conservation law following from invariance under rotations about the three-direction in charge space as well as the corresponding approximate conservation laws are derived using Noether's theorem. Examples discussed include interactions allowing the definition of "adjunct fields" (including the scalar and vector meson interactions) and an interaction leading to correction terms in order c−1.- MECHANICS: RELATIVISTIC
- PARTICLE: INTERACTION
- INTERACTION: PARTICLE
- POTENTIAL
- INVARIANCE: LORENTZ
- ISOSPIN: CLASSICAL
- CONSERVATION LAW
- SYMMETRY: rotation
- SCALAR MESON
- VECTOR MESON
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