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 'histories' of modal properties. We suggest a modification of the modal interpretation, that offers prospects of a more general applicability of the histories concept. Finally, we sketch a proposal to apply the procedure for finding histories and a many-times probability distribution to the context of algebraic quantum field theory. We show that this leads to results that are relativistically invariant. (C) 2000 Elsevier Science B.V. All rights reserved.