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How is spontaneous symmetry breaking possible?

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:
CreatorsEmailORCID
Baker, David Johndjbaker@umich.edu
Halvorson, Hanshhalvors@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: http://philsci-archive.pitt.edu/id/eprint/9860

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