On vertex algebra representations of the Schrödinger-Virasoro Lie algebra

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dc.creatorUnterberger, Jeremie
dc.date2007-03-08
dc.date2007-03-09
dc.date.accessioned2026-07-07T07:51:03Z
dc.date.available2026-07-07T07:51:03Z
dc.descriptionThe Schrödinger-Virasoro Lie algebra \mathfrak{sv} is an extension of the Virasoro Lie algebra by a nilpotent Lie algebra formed with a bosonic current of weight 3/2 and a bosonic current of weight 1. It is also a natural infinite-dimensional extension of the Schrödinger Lie algebra, which -leaving aside the invariance under time-translation - has been proved to be a symmetry algebra for many statistical physics models undergoing a dynamics with dynamical exponent z=2; it should consequently play a role akin to that of the Virasoro Lie algebra in two-dimensional equilibrium statistical physics. We define in this article general Schrödinger-Virasoro primary fields by analogy with conformal field theory, characterized by a 'spin' index and a (non-relativistic) mass, and construct vertex algebra representations of \mathfrak{sv} out of a charged symplectic boson and a free boson. We also compute two- and three-point functions of still conjectural massive fields that are defined by analytic continuation with respect to a formal parameter.
dc.description53 pages
dc.identifierhttps://arxiv.org/abs/cond-mat/0703214
dc.identifierhttp://arxiv.org/abs/cond-mat/0703214
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125377
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.titleOn vertex algebra representations of the Schrödinger-Virasoro Lie algebra
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