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

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.

arXiv commentv3., typos fixed, reference added, version appeared in JHEP

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Cited by in corpus (14)

• Carrollian and Non-relativistic Jackiw-Teitelboim Supergravity
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Three-dimensional non-relativistic extended supergravity with cosmological constant
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-Relativistic and Ultra-Relativistic Scaling Limits of Multimetric Gravity
• Three-dimensional non-relativistic supergravity and torsion
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Notes on su$(1,2)\oplus$u$(1)$ Chern-Simons theory and Torsional Newton-Cartan gravity