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 (differing in their spin) of the “exotic” particle of Duval et al. The difference between the two models is found to be sensitive to electromagnetic coupling. The nature of the noncommutative plane coordinates is discus...

The model invariant with respect to the two-fold centrally extended Galilei group proposed by Lukierski et al. can be decomposed into an infinite number of independent copies (differing in their spin) of the “exotic” particle of Duval et al. Interpreted as describing a non-relativistic anyon, this model is the non-relativistic limit of a particle with torsion related to relativistic anyons. As ...

The Galilean covariance of nonrelativistic quantum mechanics is generalized to an infinite parameter group of acceleration transformations called the Euclidean line group. Projective representations of the Euclidean line group are constructed and the resulting unitary operators are shown to implement arbitrary accelerations. These unitary operators are used to modify the time-dependent Schrödin...