Related papers: Galilean invariance in 2+1 dimensions
Some properties of central extensions of 2+1 dimensional Galilei group are discussed. It is shown that certain families of extensions are isomorphic. An interpretation of new nontrivial cocycle is offered. A few bibliographical remarks are…
We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of…
We consider the Galilean group of transformations that preserve spatial distances and absolute time intervals between events in spacetime. The special Galilean group, SGal(3), is a 10-dimensional Lie group; we examine the structure of the…
We construct the family of bilinear forms gG on R3+1 for which Galilea boosts and spatial rotations are isometries. The key feature of these bilinear forms is that they are parametrized by a Galilea invariant vector whose physical…
It is shown that equations describing the Galilean electromagnetism in the presence of sources hold invariant under the l-conformal Galilei group for an arbitrary (half)integer parameter l. The group contains transformations which link an…
We extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. We also study the…
A classification of all possible realizations of the Galilei, Galilei-similitude and Schroedinger Lie algebras in three-dimensional space-time in terms of vector fields under the action of the group of local diffeomorphisms of the space…
Some aspects of lightlike dimensional reduction in flat spacetime are studied with emphasis to classical applications. Among them the Galilean transformation of shadows induced by inertial frame changes is studied in detail by proving that,…
All deformations of two dimensional centrally extended Galilei group are classified. The corresponding quantum Lie algebras are found.
All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations…
The special Galilean group, usually denoted SGal(3), is a 10-dimensional Lie group whose important subgroups include the special orthogonal group, the special Euclidean group, and the group of extended poses. We briefly describe SGal(3) and…
We apply Mackey procedure of classifying projective systems of imprimitivity to a thorough study of the projective unitary irreducible representations of the Galilei group in 1+3 and 1+2 dimensions.
Abstract In this paper, definition of involute-evolute curve couple in Galilean space is given and some well-known theorems for the involute-evolute curves are obtained in 3-dimensional Galilean space.
We discuss a 1+1 dimensional Galilean invariant model recently introduced in connection with ultracold quantum gases. After showing its relation to a nonrelativistic 2+1 Chern-Simons matter system, we identify the generators of the…
An algebraic characterization of the contractions of the Poincar\'e group permits a proper construction of a non-relativistic limit of its tachyonic representation. We arrive at a consistent, nonstandard representation of the Galilei group…
Classical mechanics unfolds within absolute time and Euclidean space, yet our knowledge of where events occur, when they occur, and how motion evolves is inherently uncertain. The special Galilean group provides a natural setting for…
A system's invariance under Galilean transformation implies three locally conserved densities. Including them as variables, the thermodynamics is rendered explicitly frame independent, dissipative mass currents are shown to vanish, and…
We study the representations of the quantum Galilei group by a suitable generalization of the Kirillov method on spaces of non commutative functions. On these spaces we determine a quasi-invariant measure with respect to the action of the…
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)-dimensional gravity, the Galilean limit is not trivial. Depending on the…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…