How is spontaneous symmetry breaking possible?

David John Baker; Hans Halvorson

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arXiv · 1103.3227

How is spontaneous symmetry breaking possible?

David John Baker·Hans Halvorson

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Abstract

We pose and resolve a seeming paradox 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. But Wigner's theorem guarantees that every symmetry is implemented by a unitary operator that preserves transition probabilities between pure states. 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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David John Baker, Hans Halvorson. 2011-03-16. How is spontaneous symmetry breaking possible?. https://arxiv.org/abs/1103.3227

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