Abstract
We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schrödinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the extended Schrödinger algebra and provide a new higher-order Schrödinger 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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ArXiv ePrint: 2002.03558v2
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Kasikci, O., Ozdemir, N., Ozkan, M. et al. Three-dimensional higher-order Schrödinger algebras and Lie algebra expansions. J. High Energ. Phys. 2020, 67 (2020). https://doi.org/10.1007/JHEP04(2020)067
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DOI: https://doi.org/10.1007/JHEP04(2020)067