Baker, David John and Halvorson, Hans (2011) How is spontaneous symmetry breaking possible? [Preprint]

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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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Baker, David John djbaker@umich.edu Halvorson, Hans hhalvors@princeton.edu
Keywords:	algebraic quantum field theory, symmetry breaking, Wigner's theorem
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Symmetries/Invariances
Depositing User:	David Baker
Date Deposited:	03 Jul 2013 06:59
Last Modified:	03 Jul 2013 06:59
Item ID:	9860
Subjects:	Specific Sciences > Physics > Quantum Field Theory Specific Sciences > Physics > Symmetries/Invariances
Date:	2011
URI:	https://philsci-archive.pitt.edu/id/eprint/9860

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• How is spontaneous symmetry breaking possible? (deposited 14 Mar 2011 10:54)
  • How is spontaneous symmetry breaking possible? (deposited 03 Jul 2013 06:59) [Currently Displayed]

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