Abstract “Do Carroll particles move?” The answer depends on the characteristics of the
particle such as its mass, spin, electric charge, and magnetic moment. A massive Carroll …

We show how the Newton–Cartan formulation of Newtonian gravity can be obtained from
gauging the Bargmann algebra, ie the centrally extended Galilean algebra. In this gauging …

Quantum mechanics in the non-commutative plane is shown to admit the'exotic'symmetry of
the doubly centrally extended Galilei group. When coupled to a planar magnetic field whose …

The Landau problem is discussed in two similar but still different non-commutative
frameworks. The “standard” one, where the coupling to the gauge field is achieved using …

We consider a newD= 2 nonrelativistic classical mechanics model providing via the Noether
theorem the (2+ 1)-Galilean symmetry algebra with two central charges: massmand the …

A bstract We construct finite-and infinite-dimensional non-relativistic extensions of the
Newton-Hooke and Carroll (A) dS algebras using the algebra expansion method, starting …

We show that the Lukierski et al. model, invariant with respect to the two-fold centrally
extended Galilei group, can be decomposed into an infinite number of independent copies …

We define and discuss classical and quantum gravity in 2+ 1 dimensions in the Galilean
limit. Although there are no Newtonian forces between massive objects in (2+ 1) …

Owing to the two-parameter central extension of the planar Galilei group, a non relativistic
particle in the plane admits an extra structure, which yields noncommuting coordinates. For …

The “Jackiw–Nair” nonrelativistic limit of the relativistic anyon equations provides us with
infinite-component wave equations of the Dirac–Majorana–Lévy-Leblond type for the …