  An electrodynamical coupled cluster (CC) methodology starting from a
covariant formalism and an equal time approximation, and finally based on the
Dirac-Fock picture of the electron and positron fields and Coulomb gauge, is
given here. The formalism first leads to different physical interactions from
the use of an exponential cluster operator for radiative effects. Lamb, Breit
and hyperfine interactions are obtained. Next, relativistic many-body effects
are determined using the matter cluster in a way familiar from the
nonrelativistic CC. This step can be nontrivial. By allowing the matter cluster
to deviate from its traditional excitation-only form, vacuum polarization
effects are generated using the pair part of Coulomb interaction. The resulting
ground state correlation energy includes both relativistic and QED corrections,
the latter including contributions from Lamb, Breit, hyperfine and vacuum
polarization effects. The many-electron part of the theory is explicitly
formulated for closed shell species. The conservatism of the second step
indicates that extensions to multireference and state-specific cases are
possible. To illustrate the CC approach, expressions are derived for
relativistic and QED corrections to the orbital energies, configuration
energies and the ground state correlation energy in a minimal basis calculation
on noninteracting H2 molecules. Size-consistency is maintained at every step.
Because spinors of nonzero orbital angular momentum are absent, the spin-orbit
interaction and Lamb shift corrections vanish in this example. However, one
finds the kinetic energy correction, Darwin terms and corrections to the
two-electron interaction in relativistic energy values through order mc2a4Z4,
and Breit interaction energy and hyperfine splitting of levels as QED effects
through the same order. Pair energies are explicitly shown through the lowest
possible orders.
