Non-amenability and spontaneous symmetry breaking -- The hyperbolic spin-chain

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dc.creatorNiedermaier, Max
dc.creatorSeiler, Erhard
dc.date2003-12-26
dc.date2005-04-22
dc.date.accessioned2026-07-07T06:24:39Z
dc.date.available2026-07-07T06:24:39Z
dc.descriptionThe hyperbolic spin chain is used to elucidate the notion of spontaneous symmetry breaking for a non-amenable internal symmetry group, here SO(1,2). The noncompact symmetry is shown to be spontaneously broken -- something which would be forbidden for a compact group by the Mermin-Wagner theorem. Expectation functionals are defined through the L \to \infty limit of a chain of length L; the functional measure is found to have its weight mostly on configurations boosted by an amount increasing at least powerlike with L. This entails that despite the non-amenability a certain subclass of noninvariant functions is averaged to an SO(1,2) invariant result. Outside this class symmetry breaking is generic. Performing an Osterwalder-Schrader reconstruction based on the infinite volume averages one finds that the reconstructed quantum theory is different from the original one. The reconstructed Hilbert space is nonseparable and contains a separable subspace of ground states of the reconstructed transfer operator on which SO(1,2) acts in a continuous, unitary and irreducible way.
dc.description67 pages, 2 figures. Presentation changed to a more formal style, conclusions streamlined, minor errors corrected. Version accepted for publication by Annales Henri Poincar'e
dc.identifierhttps://arxiv.org/abs/hep-th/0312293
dc.identifierhttp://arxiv.org/abs/hep-th/0312293
dc.identifierAnnales Henri Poincare 6 (2005) 1025-1090
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96618
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleNon-amenability and spontaneous symmetry breaking -- The hyperbolic spin-chain
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