Condensed matter many-body theory in relativistic covariant form

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.