How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence
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How is spontaneous symmetry breaking possible? Understanding Wigner's theorem in light of unitary inequivalence. / Baker, David John; Halvorson, Hans.
In: Studies in history and philosophy of modern physics, Vol. 44, No. 4, 2013, p. 464-469.Research output: Contribution to journal › Review › Research › peer-review
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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