RELATIVISTIC CAUSALITY AND QUANTUM-MECHANICAL STATES IN THE FERMI PROBLEM

We discuss the validity of relativistic causality in the excitation ex change of a pair of atoms in vacuo. This is usually described as the F ermi problem. The atoms are modeled as two-level systems and their cou pling with the electromagnetic field is taken in the multipolar scheme and in the electric dipole approximation. The atomic dynamics is dete rmined by a solution of the Heisenberg equations for the atomic pseudo spin operators S-z, S-+ and S--, which is valid for times smaller than the spontaneous decay time. We show that for each atom this dynamics is manifestly causal, because it is independent of the presence of the other atom for times up to t = R/c, where R is the interatomic distan ce. Since this treatment is only in terms of operators and does not ma ke any reference to states, we conclude that causality is a fundamenta l feature of the Fermi problem which does not depend of the quantum-me chanical state of the atom-field system.