New Fermions at e$^+$e$^-$ Colliders: I. Production and Decay

We analyze the production in $e^+e^-$ collisions of new heavy fermions stemming from extensions of the Standard Model. We write down the most general expression for the production of two heavy fermions and their subsequent decays, allowing for the polarization of the e$^+$e$^-$ initial state and taking into account the final polarization of the fermions. We then discuss the various decay modes including cascade and three body decays, and the production mechanisms, both pair production and single production in association with ordinary fermions.