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.
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