How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence

Publikation: Bidrag til tidsskrift › Review › Forskning › fagfællebedømt

Standard

How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence. / Baker, David John; Halvorson, Hans.

I: Studies in history and philosophy of modern physics, Bind 44, Nr. 4, 2013, s. 464-469.

Publikation: Bidrag til tidsskrift › Review › Forskning › fagfællebedømt

Harvard

Baker, DJ & Halvorson, H 2013, 'How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence', Studies in history and philosophy of modern physics, bind 44, nr. 4, s. 464-469. https://doi.org/10.1016/j.shpsb.2013.09.005

APA

Baker, D. J., & Halvorson, H. (2013). How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence. Studies in history and philosophy of modern physics, 44(4), 464-469. https://doi.org/10.1016/j.shpsb.2013.09.005

Vancouver

Baker DJ, Halvorson H. How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence. Studies in history and philosophy of modern physics. 2013;44(4):464-469. https://doi.org/10.1016/j.shpsb.2013.09.005

Author

Baker, David John ; Halvorson, Hans. / How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence. I: Studies in history and philosophy of modern physics. 2013 ; Bind 44, Nr. 4. s. 464-469.

Bibtex

@article{805591f76cf34109b6a05971a474313c,

title = "How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence",

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 = "Spontaneous symmetry breaking, Inequivalent representations, Wigner's theorem, Quantum field theory",

author = "Baker, {David John} and Hans Halvorson",

year = "2013",

doi = "10.1016/j.shpsb.2013.09.005",

language = "English",

volume = "44",

pages = "464--469",

journal = "Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics",

issn = "1355-2198",

publisher = "Elsevier",

number = "4",

}

RIS

TY - JOUR

T1 - How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence

AU - Baker, David John

AU - Halvorson, Hans

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Spontaneous symmetry breaking

KW - Inequivalent representations

KW - Wigner's theorem

KW - Quantum field theory

U2 - 10.1016/j.shpsb.2013.09.005

DO - 10.1016/j.shpsb.2013.09.005

M3 - Review

VL - 44

SP - 464

EP - 469

JO - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

JF - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

SN - 1355-2198

IS - 4

ER -

ID: 289118444