Three-dimensional higher-order Schrodinger algebras and Lie algebra expansions

Kasikci O., Özdemir N., Özkan M., Zorba U.

JOURNAL OF HIGH ENERGY PHYSICS, no.4, 2020 (Peer-Reviewed Journal) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1007/jhep04(2020)067
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, INSPEC, zbMATH, Directory of Open Access Journals
  • Keywords: Chern-Simons Theories, Classical Theories of Gravity, Space-Time Symmetries


We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schrodinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the extended Schrodinger algebra and provide a new higher-order Schrodinger 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.