A Matter of Degree: Putting Unitary Inequivalence to Work

Philosophy of Science 70 (5):1329-1342 (2003)
A characteristic feature of quantum field theory is the availability of unitarily inequivalent representations of its canonical commutation relations. Under the prima facie reasonable assumption that unitary equivalence is a necessary condition for physical equivalence, this availability implies that there are many physically inequivalent quantizations of any classical field theory. To explore this dramatic non-uniqueness, and its implications for our understanding of how physical theories delimit physical possibility, I examine some of the uses to which unitarily inequivalent representations are put in another setting in which they arise: the thermodynamic limit of quantum statistical mechanics.
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DOI 10.1086/377411
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