Related papers: Nonrelativistic conformal groups and their dynamic…
We consider Schrodinger equations for a non-relativistic particle obeying N+1-th order higher derivative classical equation of motion. These equations are invariant under N(odd)-extended Galilean conformal (NGC) algebras in general d+1…
The nongeneric six- and eightdimensional orbits of SO(4,2) are described in explicitly covariant way. The relevant Hamiltonian dynamical systems are constructed and canonically quantized. It is shown that the resulting unitary…
Non-relativistic conformal (''Schr\"odinger'') symmetry is derived in a Kaluza-Klein type framework. Lightlike reduction of the massless Dirac equation from 5D Minkowski space yields L\'evy-Leblond's non-relativistic equation for a spin 1/2…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main…
The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz…
Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame,…
This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei…
The method of nonlinear realizations is applied for the conformally invariant description of the spinning particles in terms of geometrical quantities of the parameter spaces of the one dimensional N - extended superconformal groups. We…
Finite-dimensional nonrelativistic conformal Lie algebras spanned by polynomial vector fields of Galilei spacetime arise if the dynamical exponent is z=2/N with N=1,2,.... Their underlying group structure and matrix representation are…
A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local field is presented. The parametrization is…
We prove that the extended Poincare group in (1+1) dimensions is non-nilpotent solvable exponential, and therefore that it belongs to type I. We determine its first and second cohomology groups in order to work out a classification of the…
It is shown that the Schr\"{o}dinger equation for a system of interacting particles whose Compton wavelengths are of the same order of magnitude as the system size is contradictory and is not strictly nonrelativistic, because it is based on…
After the separation of the center-of-mass motion, a new privileged class of canonical Darboux bases is proposed for the non-relativistic N-body problem by exploiting a geometrical and group theoretical approach to the definition of {\it…
In two recent papers [N. Aizawa, Y. Kimura, J. Segar, J. Phys. A 46 (2013) 405204] and [N. Aizawa, Z. Kuznetsova, F. Toppan, J. Math. Phys. 56 (2015) 031701], representation theory of the centrally extended l-conformal Galilei algebra with…
The equations of motion for $N$ non-relativistic particles attracting according to Newton's law are shown to correspond to the equations for null geodesics in a $(3N+2)$-dimensional Lorentzian, Ricci-flat, spacetime with a covariantly…
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view. To this end an alternative technique of quantization outlined by the authors in a previous work and that is based in…
In non-relativistic mechanics the center of mass of an isolated system is easily separated out from the relative variables. For a N-body system these latter are usually described by a set of Jacobi normal coordinates, based on the…
We show explicitly how the Newton-Hooke groups act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes and show how…
The method of nonlinear realizations and the technique previously developed in arXiv:1208.1403 are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A…