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Three-Dimensional Higher-Order Schr\"odinger Algebras and Lie Algebra Expansions

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arxiv 2002.03558 v3 pith:KA6BGHTW submitted 2020-02-10 hep-th gr-qc

Oguzhan Kasikci , Nese Ozdemir , Mehmet Ozkan , Utku Zorba This is my paper · ORCID
classification hep-thgr-qc
keywords algebrahigher-orderodingerschralgebrasextendedparticularparameters
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We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schr\"odinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the extended Schr\"odinger algebra and provide a new higher-order Schr\"odinger algebra. The structure of this new algebra leads to a discussion on the uniqueness of the higher-order non-relativistic algebras. Especially, we show that the recent d-dimensional symmetry algebra of an action principle for Newtonian gravity is not uniquely defined but can accommodate three discrete parameters. For a particular choice of these parameters, the Bargmann algebra becomes a subalgebra of that extended algebra which allows one to introduce a mass current in a Bargmann-invariant sense to the extended theory.

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Cited by 2 Pith papers

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  1. Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory

    hep-th 2024-11 reject novelty 6.0 of 10

    An explicit conformal mapping is derived between null-reduced R times S^3 and Omega-deformed Minkowski TNC geometries, giving the state-operator generator map H0 = (R^2 H + C/R^2 - J - N)/2 in SU(1,2) non-Lorentzian CFTs.

  2. 3D Carrollian gravity from 2D Euclidean symmetry

    hep-th 2024-12 conditional novelty 4.0 of 10

    Post-Carroll-Newtonian Chern-Simons gravities are systematically obtained by semigroup-expanding 2D Euclidean B_k algebras, recovering known Carrollian models as subcases.

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