1 PI Green functions in the world - line formalism

We demonstrate, at the one-loop level, how the theory-independent part of proper N-point Green functions at finite temperature and chemical potential can be formulated in the world-line formalism, where φ 3 theory, photon scattering, effective potential in a constant magnetic field, π 0 → 2γ decay are all described in a unified way. We then derive various useful formulae and check their consistency. We also present the zero temperature limits of these formulae with the value of chemical potential kept finite.