States and observables in relativistic quantum field theories

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Abstract
We discuss two related issues pertaining to the foundations of relativistic quantum field theories. First: the question of observables; more particularly the question of what constraints, if any, are imposed upon the set of observables by the requirement of relativistic microcausality. It turns out that this requirement is in fact considerably less restrictive than has been supposed in the past. Second: the issue of physical states. We find that, in contrast to the nonrelativistic case, it is not possible to define the quantum state of a system in relativistic quantum field theories, because in this latter case no consistent description of how the state changes as the result of a measurement can be developed.