1,702 research outputs found
On Nonlocality, Lattices and Internal Symmetries
We study functional analytic aspects of two types of correction terms to the
Heisenberg algebra. One type is known to induce a finite lower bound to the resolution of distances, a short distance cutoff which is motivated
from string theory and quantum gravity. It implies the existence of families of
self-adjoint extensions of the position operators with lattices of eigenvalues.
These lattices, which form representations of certain unitary groups cannot be
resolved on the given geometry. This leads us to conjecture that, within this
framework, degrees of freedom that correspond to structure smaller than the
resolvable (Planck) scale turn into internal degrees of freedom with these
unitary groups as symmetries. The second type of correction terms is related to
the previous essentially by "Wick rotation", and its basics are here considered
for the first time. In particular, we investigate unitarily inequivalent
representations.Comment: 6 pages, LaTe
Quantum gravity effects on statistics and compact star configurations
The thermodynamics of classical and quantum ideal gases based on the
Generalized uncertainty principle (GUP) are investigated. At low temperatures,
we calculate corrections to the energy and entropy. The equations of state
receive small modifications. We study a system comprised of a zero temperature
ultra-relativistic Fermi gas. It turns out that at low Fermi energy
, the degenerate pressure and energy are lifted. The
Chandrasekhar limit receives a small positive correction. We discuss the
applications on configurations of compact stars. As increases,
the radius, total number of fermions and mass first reach their nonvanishing
minima and then diverge. Beyond a critical Fermi energy, the radius of a
compact star becomes smaller than the Schwarzschild one. The stability of the
configurations is also addressed. We find that beyond another critical value of
the Fermi energy, the configurations are stable. At large radius, the increment
of the degenerate pressure is accelerated at a rate proportional to the radius.Comment: V2. discussions on the stability of star configurations added, 17
pages, 2 figures, typos corrected, version to appear in JHE
Casimir Effect in the Presence of Minimal Lengths
It is expected that the implementation of minimal length in quantum models
leads to a consequent lowering of Planck's scale. In this paper, using the
quantum model with minimal length of Kempf et al \cite{kempf0}, we examine the
effect of the minimal length on the Casimir force between parallel plates.Comment: 10 pages, 2 figure
Harmonic oscillator with minimal length uncertainty relations and ladder operators
We construct creation and annihilation operators for harmonic oscillators
with minimal length uncertainty relations. We discuss a possible generalization
to a large class of deformations of cannonical commutation relations. We also
discuss dynamical symmetry of noncommutative harmonic oscillator.Comment: 8 pages, revtex4, final version, to appear in PR
Modelling CDA mass spectra
We present the initial results from a simulation of ion behaviour within Cassini's cosmic dust analyser (CDA) instrument, using an in-house ion dynamics code. This work is to enable and enhance the detailed interpretation of dust impact ionisation mass spectra returned from the Saturnian system. Early work has already provided insights into the properties of the impact plasma in both low- and high-velocity impacts. We find that the isotropic emission of ions from the impact plasma successfully reproduces features seen in flight spectra and that the emitted ions have a higher range of energies (tens to hundreds of eV) than previously reported in some studies. Using these new ion characteristics, we have successfully modelled CDA flight mass spectra
On the Existence of the Logarithmic Correction Term in Black Hole Entropy-Area Relation
In this paper we consider a model universe with large extra dimensions to
obtain a modified black hole entropy-area relation. We use the generalized
uncertainty principle to find a relation between the number of spacetime
dimensions and the presence or vanishing of logarithmic prefactor in the black
hole entropy-area relation. Our calculations are restricted to the
microcanonical ensembles and we show that in the modified entropy-area
relation, the microcanonical logarithmic prefactor appears only when spacetime
has an even number of dimensions.Comment: 9 Pages, No Figure
Charge Separation and Isolation in Water and Ice Particles on Strong Impacts
Tarrasó, Olga;Fuente Fuente, Carlos;Reventós, Manue
Twisted Classical Poincar\'{e} Algebras
We consider the twisting of Hopf structure for classical enveloping algebra
, where is the inhomogenous rotations algebra, with
explicite formulae given for Poincar\'{e} algebra
The comultiplications of twisted are obtained by conjugating
primitive classical coproducts by where
denotes any Abelian subalgebra of , and the universal
matrices for are triangular. As an example we show that
the quantum deformation of Poincar\'{e} algebra recently proposed by Chaichian
and Demiczev is a twisted classical Poincar\'{e} algebra. The interpretation of
twisted Poincar\'{e} algebra as describing relativistic symmetries with
clustered 2-particle states is proposed.Comment: \Large \bf 19 pages, Bonn University preprint, November 199
Motivic Serre invariants, ramification, and the analytic Milnor fiber
We show how formal and rigid geometry can be used in the theory of complex
singularities, and in particular in the study of the Milnor fibration and the
motivic zeta function. We introduce the so-called analytic Milnor fiber
associated to the germ of a morphism f from a smooth complex algebraic variety
X to the affine line. This analytic Milnor fiber is a smooth rigid variety over
the field of Laurent series C((t)). Its etale cohomology coincides with the
singular cohomology of the classical topological Milnor fiber of f; the
monodromy transformation is given by the Galois action. Moreover, the points on
the analytic Milnor fiber are closely related to the motivic zeta function of
f, and the arc space of X.
We show how the motivic zeta function can be recovered as some kind of Weil
zeta function of the formal completion of X along the special fiber of f, and
we establish a corresponding Grothendieck trace formula, which relates, in
particular, the rational points on the analytic Milnor fiber over finite
extensions of C((t)), to the Galois action on its etale cohomology.
The general observation is that the arithmetic properties of the analytic
Milnor fiber reflect the structure of the singularity of the germ f.Comment: Some minor errors corrected. The original publication is available at
http://www.springerlink.co
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