An effective Dirac equation for a binary of two fermions

Effective Dirac equations are, by following the work of Pilkuhn, derived for a binary of two fermions from the original two-fermion Dirac-type Hamiltonian written in a 16-component spinor representation. For spherical interaction potential (like the static Coulomb potential) the spin dynamics in the product spin space and spatial dynamics in the particle–antiparticle state space can be fully decoupled and separated. The case of atomic hydrogen is solved again as an example, and the standard results including recoil effects through the reduced mass and fine structure induced by spin–orbit coupling are recovered for the energy spectrum.

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