Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QED

Details Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QED Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QED

2003-03-27

arxiv.org/abs/hep-th/0303250v2

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1063/1.1649794

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.

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