8 research outputs found

### Casimir-Polder intermolecular forces in minimal length theories

Generalized uncertainty relations are known to provide a minimal length
$\hbar\sqrt{\beta}$. The effect of such minimal length in the Casimir-Polder
interactions between neutral atoms (molecules) is studied. The first order
correction term in the minimal uncertainty parameter is derived and found to
describe an attractive potential scaling as $r^{-9}$ as opposed to the well
known $r^{-7}$ long range retarded potential.Comment: 1 Figure. Version published by Physical Review D. Few references
added, typos correcte

### Cosmological Constraints on a Dynamical Electron Mass

Motivated by recent astrophysical observations of quasar absorption systems,
we formulate a simple theory where the electron to proton mass ratio $\mu
=m_{e}/m_{p}$ is allowed to vary in space-time. In such a minimal theory only
the electron mass varies, with $\alpha$ and $m_{p}$ kept constant. We find
that changes in $\mu$ will be driven by the electronic energy density after
the electron mass threshold is crossed. Particle production in this scenario is
negligible. The cosmological constraints imposed by recent astronomical
observations are very weak, due to the low mass density in electrons. Unlike in
similar theories for spacetime variation of the fine structure constant, the
observational constraints on variations in $\mu$ imposed by the weak
equivalence principle are much more stringent constraints than those from
quasar spectra. Any time-variation in the electron-proton mass ratio must be
less than one part in $10^{9}$since redshifts $z\approx 1.$This is more than
one thousand times smaller than current spectroscopic sensitivities can
achieve. Astronomically observable variations in the electron-proton must
therefore arise directly from effects induced by varying fine structure
'constant' or by processes associated with internal proton structure. We also
place a new upper bound of $2\times 10^{-8}$ on any large-scale spatial
variation of $\mu$ that is compatible with the isotropy of the microwave
background radiation.Comment: New bounds from weak equivalence principle experiments added,
conclusions modifie

### Relativistic Green functions in a plane wave gravitational background

We consider a massive relativistic particle in the background of a
gravitational plane wave. The corresponding Green functions for both spinless
and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti
\cite{Barducci3}, are reobtained here by alternative methods, as for example,
the Fock-Schwinger proper-time method and the algebraic method. In analogy to
the electromagnetic case, we show that for a gravitational plane wave
background a semiclassical approach is also sufficient to provide the exact
result, though the lagrangian involved is far from being a quadratic one.Comment: Last paper by Professor Arvind Narayan Vaidya, 18 pages, no figure

### Graphene and non-Abelian quantization

In this article we employ a simple nonrelativistic model to describe the low
energy excitation of graphene. The model is based on a deformation of the
Heisenberg algebra which makes the commutator of momenta proportional to the
pseudo-spin. We solve the Landau problem for the resulting Hamiltonian which
reduces, in the large mass limit while keeping fixed the Fermi velocity, to the
usual linear one employed to describe these excitations as massless Dirac
fermions. This model, extended to negative mass, allows to reproduce the
leading terms in the low energy expansion of the dispersion relation for both
nearest and next-to-nearest neighbor interactions. Taking into account the
contributions of both Dirac points, the resulting Hall conductivity, evaluated
with a $\zeta$-function approach, is consistent with the anomalous integer
quantum Hall effect found in graphene. Moreover, when considered in first order
perturbation theory, it is shown that the next-to-leading term in the
interaction between nearest neighbor produces no modifications in the spectrum
of the model while an electric field perpendicular to the magnetic field
produces just a rigid shift of this spectrum.
PACS: 03.65.-w, 81.05.ue, 73.43.-fComment: 23 pages, 4 figures. Version to appear in the Journal of Physics A.
The title has been changed into "Graphene and non-Abelian quantization". The
motivation and presentation of the paper has been changed. An appendix and
Section 6 on the evaluation of the Hall conductivity have been added.
References adde