Quantum and classical relativistic energy states in stationary geometries

The positive and negative root states (E⁺, E^?) for a particle moving along a geodesic in a stationary background, introduced by Christodoulou and Ruffini, are here interpreted in the framework of a relativistic quantum field theory. It is shown how E⁺ and E^? have to be considered as the classical correspondent of the positive and negative energy states of a quantized field. It is explicitly shown that crossing between the states E⁺ and E^? can occur and consequently the necessary condition for particle creation as given by Klein, Sauter, Heisenberg and Euler can be encountered.