Authors
Hans Halvorson
Princeton University
Abstract
We pose and resolve a puzzle about spontaneous symmetry breaking in the quantum theory of infinite systems. For a symmetry to be spontaneously broken, it must not be implementable by a unitary operator in a ground state's GNS representation. But Wigner's theorem guarantees that any symmetry's action on states is given by a unitary operator. How can this unitary operator fail to implement the symmetry in the GNS representation? We show how it is possible for a unitary operator of this sort to connect the folia of unitarily inequivalent representations. This result undermines interpretations of quantum theory that hold unitary equivalence to be necessary for physical equivalence.
Keywords philosophy of physics  quantum field theory
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DOI 10.1016/j.shpsb.2013.09.005
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References found in this work BETA

Interpreting Quantum Field Theory.Laura Ruetsche - 2002 - Philosophy of Science 69 (2):348-378.
Broken Symmetry and Spacetime.David John Baker - 2011 - Philosophy of Science 78 (1):128-148.
Explaining Quantum Spontaneous Symmetry Breaking.Chuang Liu & Gérard G. Emch - 2005 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1):137-163.
Johnny’s So Long at the Ferromagnet.Laura Ruetsche - 2006 - Philosophy of Science 73 (5):473-486.

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On Broken Symmetries and Classical Systems.Benjamin Feintzeig - 2015 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52 (Part B):267-273.

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