288 research outputs found
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
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
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
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
and an expansion scalar . 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 . 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 for redshifts .Comment: 17 pages, enlarged version, accepted by Phys. Rev.
Berry phase correction to electron density in solids and "exotic" dynamics
Recent results on the semiclassical dynamics of an electron in a solid are
explained using techniques developed for ``exotic'' Galilean dynamics. The
system is indeed Hamiltonian and Liouville's theorem holds for the symplectic
volume form. Suitably defined quantities satisfy hydrodynamic equations.Comment: Affiliation of the first Author expanded. One more reference added.
To appear in Mod. Phys. Lett. B. 5 page
Noncommutative planar particle dynamics with gauge interactions
We consider two ways of introducing minimal Abelian gauge interactions into the model presented in [Ann. Phys. 260 (1997) 224]. These two approaches are different only if the second central charge of the planar Galilei group is nonzero. One way leads to the standard gauge transformations and the other one to a generalised gauge theory with gauge transformations accompanied by time-dependent area-preserving coordinate transformations. Both approaches, however, are related to each other by a classical Seiberg–Witten map supplemented by a noncanonical transformation of the phase space variables for planar particles. We also formulate the two-body problem in the model with our generalised gauge symmetry and consider the case with both CS and background electromagnetic fields, as it is used in the description of fractional quantum Hall effect
Dynamics of railway freight vehicles
This paper summarises the historical development of railway freight vehicles and how vehicle designers have tackled the difficult challenges of producing running gear which can accommodate the very high tare to laden mass of typical freight wagons whilst maintaining stable running at the maximum required speed and good curving performance. The most common current freight bogies are described in detail and recent improvements in techniques used to simulate the dynamic behaviour of railway vehicles are summarised and examples of how these have been used to improve freight vehicle dynamic behaviour are included. A number of recent developments and innovative components and sub systems are outlined and finally two new developments are presented in more detail: the LEILA bogie and the SUSTRAIL bogie
Supersymmetrization of the Radiation Damping
We construct a supersymmetrized version of the model to the radiation damping
\cite{03} introduced by the present authors \cite{ACWF}. We dicuss its
symmetries and the corresponding conserved Noether charges. It is shown this
supersymmetric version provides a supersymmetric generalization of the Galilei
algebra obtained in \cite{ACWF}. We have shown that the supersymmetric action
can be splited into dynamically independent external and internal sectors.Comment: 9 page
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