Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QED

Abstract

We present a variational method for deriving relativistic two-fermion wave equations in a Hamiltonian formulation of QED. A reformulation of QED is performed, in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. The reformulation permits one to use a simple Fock-space variational trial state to derive relativistic fermion-antifermion wave equations from the corresponding quantum field theory. We verify that the energy eigenvalues obtained from the wave equation agree with known results for positronium.

25 pages, accepted in Journal of Mathematical Physics (2004)

References in corpus (1)

• A variational calculation of particle-antiparticle bound states in the scalar Yukawa model

Cited by in corpus (5)

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• Relativistic wave equations of n-body systems of fermions and antifermions of various masses in quantum electrodynamics
• Two fermion relativistic bound states: hyperfine shifts
• Bound-State Variational Wave Equation For Fermion Systems In QED
• Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model