Gauging of 1d-space translations for nonrelativistic point particles

Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the introduction of two gauge fields whose minimal self interaction leads to a Maxwellian term in the Lagrangean. No dilaton field is introduced. We fix the gauge such that the residual symmetry group is the Galilei group. In case of a line the two-particle reduced Lagrangean describes the motion in a Newtonian gravitational potential with strength proportional to the energy. For particles on a circle with certain initial conditions we only have a collective rotation with constant angular velocity.Comment: 10 pages, Late

Analytical solutions for two inhomogeneous cosmological models with energy flow and dynamical curvature

Recently we have introduced a nonrelativistic cosmological model (NRCM) exhibiting a dynamical spatial curvature. For this model the present day cosmic acceleration is not attributed to a negative pressure (dark energy) but it is driven by a nontrivial energy flow leading to a negative spatial curvature. In this paper we generalize the NRCM in two different ways to the relativistic regime and present analytical solutions of the corresponding Einstein equations. These relativistic models are characterized by two inequivalent extensions of the FLWR metric with a time-dependent curvature function $K (t)$ and an expansion scalar $a(t)$. The fluid flow is supposed to be geodesic. The model V1 is shear-free with isotropic pressure and therefore conformal flat. In contrast to V1 the second model V2 shows a nontrivial shear and an anisotropic pressure. For both models the inhomogeneous solutions of the corresponding Einstein equations will agree in leading order at small distances with the NRCM if a(t) and K(t) are each identical with those determined in the NCRM. Then the metric is completely fixed by three constants. The arising energy momentum tensor contains a nontrivial energy flow vector. Our models violate locally the weak energy condition. Global volume averaging leads to explicit expressions for the effective scale factor and the expansion rate $H (z)$. Backreaction effects cancel each other for the model V2 but they are nonzero and proportional to the square of the magnitude of the energy flow for the model V1. The large scale (relativistic) corrections to the NCRM results are small for the model V2 for a small-sized energy flow. We have reproduced a corresponding adjustment of the three free constants from [1] to cosmic chronometer data leading to the prediction of an almost constant, negative value for the dimensionless curvature function $k(z) \sim - 1$ for redshifts $z < 2$.Comment: 17 pages, enlarged version, accepted by Phys. Rev.

Chern-Simons Particles with Nonstandard Gravitational Interaction

The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparametrization invariant way, to a translational Chern-Simons action. The quantum two-body problem is described by a nonstandard Schr\"{o}dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels.Comment: LaTeX, 1 figure (included), 14 page

Exotic galilean symmetry and non-commutative mechanics

Some aspects of the "exotic" particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized non-commutative models are also discussed. Minimal as well as anomalous coupling to an external electromagnetic field is presented. Supersymmetric extension is also considered. Exotic Galilean symmetry is also found in Moyal field theory. Similar equations arise for a semiclassical Bloch electron, used to explain the anomalous/spin/optical Hall effects.Comment: Review paper. Published versio