Acceleration-Enlarged Symmetries in Nonrelativistic Space-Time with a Cosmological Constant

TL;DR

This paper explores the extension of Newton-Hooke symmetries in nonrelativistic space-time with a cosmological constant by adding acceleration generators, leading to new algebraic structures and non-commutative phase spaces.

Contribution

It introduces an enlarged NH symmetry algebra with acceleration generators and central extensions, providing a classical framework for models with these symmetries.

Findings

Enlarged NH algebra includes acceleration generators and central extensions.

Models exhibit non-commutative phase space structures.

System reduces to acceleration-enlarged Galilean symmetry when cosmological constant vanishes.

Abstract

By considering the nonrelativistic limit of de-Sitter geometry one obtains the nonrelativistic space-time with a cosmological constant and Newton-Hooke (NH) symmetries. We show that the NH symmetry algebra can be enlarged by the addition of the constant acceleration generators and endowed with central extensions (one in any dimension (D) and three in D=(2+1)). We present a classical Lagrangian and Hamiltonian framework for constructing models quasi-invariant under enlarged NH symmetries which depend on three parameters described by three nonvanishing central charges. The Hamiltonian dynamics then splits into external and internal sectors with new non-commutative structures of external and internal phase spaces. We show that in the limit of vanishing cosmological constant the system reduces to the one presented in [1] which possesses accelaration-enlarged Galilean symmetries.