Consistent histories and relativistic invariance in the modal interpretation of quantum mechanics

Modal interpretations of quantum mechanics assign definite properties to physical systems and specify single-time joint probabilities of these properties. We show that a natural extension, applying to properties at several times, can be given if a decoherence condition is satisfied. This extension defines "consistent histories" of modal properties. We suggest a new form of the modal scheme, that offers prospects of a more general applicability of the histories concept. Finally, we discuss a possible way of applying these ideas to relativistic quantum field theory.