Eight-component two-fermion equations

An eight-component formalism is proposed for the relativistic two-fermion problem. In QED, it extends the applicability of the Dirac equation with hyperfine interaction to the positronium case. The use of exact relativistic two-body kinematics entails a CP-invariant spectrum which is symmetric in the total cms energy. It allows the extension of recent \alpha^6 recoil corrections to the positronium case, and implies new recoil corrections to the fine and hyperfine structures and to the Bethe logarithm.Comment: Revtex, accepted for publication in Phys. Rev.

Eight-Component Differential Equation for Leptonium

It is shown that the potential for lepton-antilepton bound states (leptonium) is the Fourier transform of the first Born approximation to the QED scattering amplitude in an 8-component equation, while 16-component equations are excluded. The Fourier transform is exact at all cms energies \Gamma1 ! E ! 1; the resulting atomic spectrum is explicitly CPT-invariant. PACS number: 03.65.Pm ----------- Fax: +49-721-370726 Internet: [email protected] [email protected] [email protected] I. INTRODUCTION In muonium e \Gamma ¯ + , the mass m 2 of the heavier particle is so large that the kinetic energy p 2 2 =2m 2 can be added as a recoil correction to the electron's Dirac Hamiltonian. The resulting Dirac equation has 8 components, with the Pauli matrices oe 2 in the hyperfine operator [1,2]. However, a similar 8--component equation exists which avoids the expansion in terms of 1=m 2 [3,4]. Despite its asymmetric form, it reproduces the..

Eight-Component Two-Fermion Equations

An eight-component formalism is proposed for the relativistic two-fermion problem. In QED, it extends the applicability of the Dirac equation with hyperfine interaction to the positronium case. The use of exact relativistic two-body kinematics entails a CP-invariant spectrum which is symmetric in the total cms energy. It allows the extension of recent ff 6 recoil corrections to the positronium case, and implies new recoil corrections to the fine and hyperfine structures and to the Bethe logarithm. PACS number: 03.65.Pm I. INTRODUCTION The relativistic two-body problem for two spin-1=2 particles is based on 16-component wave functions which transform as the direct product of two four-component Dirac spinors, / (16) ¸ / 1\Omega / 2 . For unequal masses m 2 ? m 1 , the equations are simplified by the elimination of the small components of particle 2 and by a subsequent power series expansion about the non-relativistic limit of this particle. One thus obtains an effective Dirac equ..