On spontaneous breaking of continuous symmetry in 1+1-dimensional space-time

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dc.creatorFaber, M.
dc.creatorIvanov, A. N.
dc.date2002-04-29
dc.date2003-06-29
dc.date.accessioned2026-07-07T04:13:27Z
dc.date.available2026-07-07T04:13:27Z
dc.descriptionWe analyse Coleman's theorem asserting the absence Goldstone bosons and spontaneously broken continuous symmetry in the quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-time (Comm. Math. Phys. 31, 259 (1973)). We confirm that Coleman's theorem reproduces well-known Wightman's statement about the non-existence of a quantum field theory of a free massless (pseudo)scalar field in 1+1-dimensional space-time in terms of Wightman's observables defined on the test functions from S(R^2). Referring to our results (Eur. Phys. J. C 24, 653 (2002)) we argue that a formulation of a quantum field theory of a free massless (pseudo)scalar field in terms of Wightman's observables defined on the test functions from S_0(R^2) is motivated well by the possibility to remove a collective zero-mode motion of the ``center of mass'' of a free massless (pseudo)scalar field (Eur. Phys. J. C 24, 653 (2002)) responsible for infrared divergences of the Wightman functions. We show that in the quantum field theory of a free massless (pseudo)scalar field with Wightman's observables defined on the test functions from S_0(R^2) a continuous symmetry is spontaneously broken. Coleman's theorem reformulated for the test functions from S_0(R^2) does not refute this result. We construct a most general version of a quantum field theory of a self-coupled massless (pseudo)scalar field with a conserved current. We show that this theory satisfies Wightman's axioms and Wightman's positive definiteness condition with Wightman's observables defined on the test functions from S(R^2) and possesses spontaneously broken continuous symmetry. Nevertheless, in this theory the generating functional of Green functions exists only when the collective zero-mode is not excited by the external source.
dc.description27pages, Latex, no figures, title is changed and text is revised
dc.identifierhttps://arxiv.org/abs/hep-th/0204237
dc.identifierhttp://arxiv.org/abs/hep-th/0204237
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/51263
dc.subjectHigh Energy Physics - Theory
dc.titleOn spontaneous breaking of continuous symmetry in 1+1-dimensional space-time
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