Why Be Regular? Part II

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Feintzeig, Benjamin H.; Weatherall, James Owen
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preprint description
We provide a novel perspective on "regularity" as a property of representations of the Weyl algebra. In Part I, we critiqued a proposal by Halvorson [2004, "Complementarity of representations in quantum mechanics", Studies in History and Philosophy of Modern Physics 35(1), pp. 45--56], who advocates for the use of the non-regular "position" and "momentum" representations of the Weyl algebra. Halvorson argues that the existence of these non-regular representations demonstrates that a quantum mechanical particle can have definite values for position or momentum, contrary to a widespread view. In this sequel, we propose a justification for focusing on regular representations, pace Halvorson, by drawing on algebraic methods.