  We present a relativistic covariant form of many-body theory. The many-body
covariant Lagrangian is derived from QED by integrating out the internal
non-quantized electromagnetic field. The ordinary many-body Hamiltonian is
recovered as an approximation to the exact covariant theory that contains
many-body terms beyond the solely electrostatic interaction, e.g. the Lorentz
force among electrons, spin-spin etc. Spin and relativistic terms, e.g.
spin-orbit, are also automatically accounted. Moreover, the theory is compact,
gauge-invariant and respects causality.
