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arXiv · 2002.03558

Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions

Oguzhan Kasikci·Nese Ozdemir·Mehmet Ozkan·Utku Zorba
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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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Oguzhan Kasikci, Nese Ozdemir, Mehmet Ozkan, Utku Zorba. 2020-04-14. Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions. https://doi.org/10.1007/jhep04(2020)067%2010.1007%2Fjhep04(2020)067%2010.1007%2Fjhep04(2020)067

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