 In quantum field theory, however, von Neumann’s uniqueness theorem loses its validity since here one is dealing with an infinite number of degrees of freedom. Now one is confronted with a multitude of unitarily inequivalent representations (UIRs)  of the CCRs and it is not obvious what this means physically and how one should cope with it. Since the troublesome inequivalent representations of the CCRs that arise in QFT are all irreducible their inequivalence is not due to the fact that some are reducible while others are not (a representation is reducible if there is an invariant subrepresentation, i.e. a subset which alone represent the CCRs already). Since unitarily inequivalent representations seem to describe different physical states of affairs it would no longer be legitimate to simply choose the most convenient representation, just like choosing the most convenient frame of reference. In principle all but one of the UIRs could be physically irrelevant, i.e. mathematical artefacts of a redundant formalism. However, it seems that at least some irreducible representations of the CCRs are inequivalent and physically relevant.