27 research outputs found
Nonstandard approach to gravity for the dark sector of the Universe
We summarize the present state of research on the darkon fluid as a model for the dark sector of the Universe. Nonrelativistic massless particles are introduced as a realization of the Galilei group in an enlarged phase space. The additional degrees of freedom allow for a nonstandard, minimal coupling to gravity respecting Einstein’s equivalence principle. Extended to a self-gravitating fluid the Poisson equation for the gravitational potential contains a dynamically generated effective gravitational mass density of either sign. The equations of motion (EOMs) contain no free parameters and are invariant w.r.t. Milne gauge transformations. Fixing the gauge eliminates the unphysical degrees of freedom. The resulting Lagrangian possesses no free particle limit. The particles it describes, darkons, exist only as fluid particles of a self-gravitating fluid. This darkon fluid realizes the zero-mass Galilean algebra extended by dilations with dynamical exponent z = 5/3 . We reduce the EOMs to Friedmann-like equations and derive conserved quantities and a unique Hamiltonian dynamics by implementing dilation symmetry. By the Casimir of the Poisson-bracket (PB)-algebra we foliate the phase space and construct a Lagrangian in reduced phase space. We solve the Friedmann-like equations with the transition redshift and the value of the Casimir as integration constants. We obtain a deceleration phase for the early Universe and an acceleration phase for the late Universe in agreement with observations. Steady state equations in the spherically symmetric case may model a galactic halo. Numerical solutions of a nonlinear differential equation for the gravitational potential lead to predictions for the dark matter (DM) part of the rotation curves (RCs) of galaxies in qualitative agreement with observational data. We also present a general covariant generalization of the model
Gauging of 1d-space translations for nonrelativistic matter - geometric bags
We develop in a systematic fashion the idea of gauging 1d-space translations
with fixed Newtonian time for nonrelativistic matter (particles and fields). By
starting with a nonrelativistic free theory we obtain its minimal gauge
invariant extension by introducing two gauge fields with a Maxwellian self
interaction. We fix the gauge so that the residual symmetry group is the
Galilei group and construct a representation of the extended Galilei algebra.
The reduced N-particle Lagrangian describes geodesic motion in a
(N-1)-dimensional (Pseudo-) Riemannian space. The singularity of the metric for
negative gauge coupling leads in classical dynamics to the formation of
geometric bags in the case of two or three particles. The ordering problem
within the quantization scheme for -particles is solved by canonical
quantization of a pseudoclassical Schroedinger theory obtained by adding to the
continuum generalization of the point-particle Lagrangian an appropriate
quantum correction. We solve the two-particle bound state problem for both
signs of the gauge coupling. At the end we speculate on the possible physical
relevance of the new interaction induced by the gauge fields.Comment: 28 pages, LaTe
Moving vortices in noncommutative gauge theory
Exact time-dependent solutions of nonrelativistic noncommutative Chern -
Simons gauge theory are presented in closed analytic form. They are different
from (indeed orthogonal to) those discussed recently by Hadasz, Lindstrom,
Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary
constant velocity, and can be obtained from the previously known static
solutions by the recently found ``exotic'' boost symmetry.Comment: Latex, 6 pages, no figures. A result similar to ours was obtained,
independently, by Hadasz et al. in the revised version of their pape
Deformed Chern-Simons interaction for nonrelativistic point particles
We deform the interaction between nonrelativistic point particles on a plane
and a Chern-Simons field to obtain an action invariant with respect to
time-dependent area-preserving diffeomorphisms. The deformed and undeformed
Lagrangians are connected by a point transformation leading to a classical
Seiberg-Witten map between the corresponding gauge fields. The Schroedinger
equation derived by means of Moyal-Weyl quantization from the effective
two-particle interaction exhibits - a singular metric, leading to a splitting
of the plane into an interior (bag-) and an exterior region, - a singular
potential (quantum correction) with singularities located at the origin and at
the edge of the bag. We list some properties of the solutions of the radial
Schroedinger equation.Comment: 7 pages, LaTeX Some references adde
N=2 Supersymmetric Planar Particles and Magnetic Interaction from Noncommutativity
We describe a N=2 supersymmetric extension of the nonrelativistic
(2+1)-dimensional model describing particles on the noncommutative plane with
scalar (electric) and vector (magnetic) interactions.
First, we employ the N=2 superfield technique and show that in the presence
of a scalar N=2 superpotential the magnetic interaction is implied by the
presence of noncommutativity of position variables. Further, by expressing the
supersymmetric Hamiltonian as a bilinear in N=2 supercharges we obtain two
supersymmetric models with electromagnetic interactions and two different
noncanonical symplectic structures describing noncommutativity. We show that
both models are related by a map of the Seiberg-Witten type.Comment: LaTeX,12 pages.Minor corrections; version appears in PL
Acceleration-Extended Galilean Symmetries with Central Charges and their Dynamical Realizations
We add to Galilean symmetries the transformations describing constant
accelerations. The corresponding extended Galilean algebra allows, in any
dimension , the introduction of one central charge while in
we can have three such charges: c, \theta and \theta'.
We present nonrelativistic classical mechanics models, with higher order time
derivatives and show that they give dynamical realizations of our algebras. The
presence of central charge requires the acceleration square Lagrangian
term. We show that the general Lagrangian with three central charges can be
reinterpreted as describing an exotic planar particle coupled to a dynamical
electric and a constant magnetic field.Comment: LaTeX, 13 pages. V2: Section 4 shortened. The version in print in
Physics Letters
Enlarged Galilean symmetry of anyons and the Hall effect
Enlarged planar Galilean symmetry, built of both space-time and field
variables and also incorporating the ``exotic'' central extension is
introduced. It is used to describe non-relativistic anyons coupled to an
electromagnetic field. Our theory exhibits an anomalous velocity relation of
the type used to explain the Anomalous Hall Effect. The Hall motions,
characterized by a Casimir of the enlarged algebra, become mandatory for some
critical value(s) of the magnetic field. The extension of our scheme yields the
semiclassical effective model of the Bloch electron.Comment: LaTeX, 7 pages. No figures. One more reference adde
From Gauging Nonrelativistic Translations to N-Body Dynamics
We consider the gauging of space translations with time-dependent gauge
functions. Using fixed time gauge of relativistic theory, we consider the
gauge-invariant model describing the motion of nonrelativistic particles. When
we use gauge-invariant nonrelativistic velocities as independent variables the
translation gauge fields enter the equations through a d\times (d+1) matrix of
vielbein fields and their Abelian field strengths, which can be identified with
the torsion tensors of teleparallel formulation of relativity theory. We
consider the planar case (d=2) in some detail, with the assumption that the
action for the dreibein fields is given by the translational Chern-Simons term.
We fix the asymptotic transformations in such a way that the space part of the
metric becomes asymptotically Euclidean. The residual symmetries are (local in
time) translations and rigid rotations. We describe the effective interaction
of the d=2 N-particle problem and discuss its classical solution for N=2. The
phase space Hamiltonian H describing two-body interactions satisfies a
nonlinear equation H={\cal H}(\vec x,\vec p;H) which implies, after
quantization, a nonstandard form of the Schr\"odinger equation with energy
dependent fractional angular momentum eigenvalues. Quantum solutions of the
two-body problem are discussed. The bound states with discrete energy levels
correspond to a confined classical motion (for the planar distance between two
particles r\le r_0) and the scattering states with continuum energy correspond
to the classical motion for r>r_0. We extend our considerations by introducing
an external constant magnetic field and, for N=2, provide the classical and
quantum solutions in the confined and unconfined regimes.Comment: LaTeX, 38 pages, 1 picture include
Galilean symmetry in noncommutative field theory
When the interaction potential is suitably reordered, the Moyal field theory
admits two types of Galilean symmetries, namely the conventional
mass-parameter-centrally-extended one with commuting boosts, but also the
two-fold centrally extended ``exotic'' Galilean symmetry, where the commutator
of the boosts yields the noncommutative parameter. In the free case, one gets
an ``exotic'' two-parameter central extension of the Schroedinger group. The
conformal symmetry is, however, broken by the interaction.Comment: Corrected version. Further remarks and references added. LaTex, 8
pages, no figure
Acceleration-Enlarged Symmetries in Nonrelativistic Space-Time with a Cosmological Constant
By considering the nonrelativistic limit of de-Sitter geometry one obtains
the nonrelativistic space-time with a cosmological constant and Newton-Hooke
(NH) symmetries. We show that the NH symmetry algebra can be enlarged by the
addition of the constant acceleration generators and endowed with central
extensions (one in any dimension (D) and three in D=(2+1)). We present a
classical Lagrangian and Hamiltonian framework for constructing models
quasi-invariant under enlarged NH symmetries which depend on three parameters
described by three nonvanishing central charges. The Hamiltonian dynamics then
splits into external and internal sectors with new non-commutative structures
of external and internal phase spaces. We show that in the limit of vanishing
cosmological constant the system reduces to the one presented in [1] which
possesses accelaration-enlarged Galilean symmetries.Comment: 13 pages; small changes like a couple of footnotes et