Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes

Higher-derivative mechanics with N=2 l-conformal Galilei supersymmetry

The analysis previously developed in [J. Math. Phys. 55 (2014) 102901] is used to construct systems which hold invariant under N=2 l-conformal Galilei superalgebra. The models describe two different supersymmetric extensions of a free higher-derivative particle. Their Newton-Hooke counterparts are derived by applying appropriate coordinate transformations.

Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator

Dynamical systems invariant under the action of the l-conformal Newton-Hooke algebras are constructed by the method of nonlinear realizations. The relevant first order Lagrangians together with the corresponding Hamiltonians are found. The relation to the Galajinsky and Masterov [Phys. Lett. B 723 (2013) 190] approach as well as the higher derivatives formulation is discussed. The generalized Niederer's transformation are presented which relate the systems under consideration to those invariant under the action of the l-conformal Galilei algebra [Nucl. Phys. B 876 (2013) 309]. As a nice applic…

Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry

In this thesis some systems with exotic symmetries, which are a peculiarity in 2+1 space-time dimensions, are studied. Coded in the exotic structure, there appear noncommutative coordinates and a phases structure. This kind of systems has attracted attention from different areas of physics independently. Among them, we can mention: theory of ray representations of Lie groups, anyon physics, some condensed matter systems, for instance the quantum Hall effect, planar gauge and gravitation theories, noncommutative field theory, noncommutative geometry, and noncommutative quantum mechanics. We foc…

Mechanics and Newton-Cartan-Like Gravity on the Newton-Hooke Space-time

We focus on the dynamical aspects of Newton-Hooke space-time ${\cal NH}_+$ mainly from the viewpoint of geometric contraction of the de Sitter spacetime. We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton's gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schrödinger equation from the geometric contraction, where we can relate the conservative probability i…

Lorentzian Snyder spacetimes and their Galilei and Carroll limits from projective geometry

We show that the Lorentzian Snyder models, together with their Galilei and Carroll limiting cases, can be rigorously constructed through the projective geometry description of Lorentzian, Galilean and Carrollian spaces with nonvanishing constant curvature. The projective coordinates of such curved spaces take the role of momenta, while translation generators over the same spaces are identified with noncommutative spacetime coordinates. In this way, one obtains a deformed phase space algebra, which fully characterizes the Snyder model and is invariant under boosts and rotations of the relevant …

Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a "relativity group" which is a one-parameter family of deformations of the standard Galilei group to the Newton-Hooke group which is a Wigner-Inonu contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn's theorem and related results. Larmor's Theorem is used to show that the one-parameter fami…

Conformal and projective symmetries in Newtonian cosmology

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent…

具有非相对论规范超对称性的完美流体方程

Perfect fluid equations with nonrelativistic conformal supersymmetries

本文扩展了之前关于构建具有N=1,2 Schrödinger超对称性的完美流体方程的结果，考虑了其他类型的非相对论规范超对称性，构建了超对称流体模型，并讨论了构造完美流体方程的细微差别。