A Tale of Three Equations: Breit, Eddington-Guant, and Two-Body Dirac

Abstract

G.Breit's original paper of 1929 postulates the Breit equation as a correction to an earlier defective equation due to Eddington and Gaunt, containing a form of interaction suggested by Heisenberg and Pauli. We observe that manifestly covariant electromagnetic Two-Body Dirac equations previously obtained by us in the framework of Relativistic Constraint Mechanics reproduce the spectral results of the Breit equation but through an interaction structure that contains that of Eddington and Gaunt. By repeating for our equation the analysis that Breit used to demonstrate the superiority of his equation to that of Eddington and Gaunt, we show that the historically unfamiliar interaction structures of Two-Body Dirac equations (in Breit-like form) are just what is needed to correct the covariant Eddington Gaunt equation without resorting to Breit's version of retardation.

15 pages latex, published in Foundations of Physics, Vol 27, 67 (1997)

Cited by in corpus (13)

• Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction
• Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
• Multi-Time Schrödinger Equations Cannot Contain Interaction Potentials
• Exact solution of an exciton energy for a monolayer medium
• Multi-Time Wave Functions
• Two body relativistic wave equations
• The relativistic dynamics of oppositely charged two fermions interacting with external uniform magnetic field
• Consistency Proof for Multi-Time Schrodinger Equations with Particle Creation and Ultraviolet Cut-Off
• On the question of current conservation for the Two-Body Dirac equations of constraint theory
• Relativistic action-at-a-distance interactions: Lagrangian and Hamiltonian to terms of second order
• Properties of the Anomalous States of Positronium
• Anomalous states of positronium
• A derivation of the Breit equation from Barut's covariant formulation of electrodynamics in terms of direct interactions