Particle interpretation of the Dirac–Coulomb solutions

Abstract

The Dirac Hamiltonian with an external Coulomb field is considered in Fock space; it contains an even part that conserves the number of fermion–antifeimion pairs and an odd part that permits pair annihilation and creation. By successive unitary transformations the nondiagonal terms connecting subspaces with different numbers of pairs can be removed order by order in an (1/m) expansion and the effective no-pair Hamiltonian can be explicitly constructed. If all disconnected graphs are excluded the result is then identical to the result obtained by a similar procedure applied to the Dirac–Coulomb one particle problem in relativistic quantum mechanics.