24,985 research outputs found
Solving the noncommutative Batalin-Vilkovisky equation
I show that a summation over ribbon graphs with legs gives the construction
of the solutions to the noncommutative Batalin-Vilkovisky equation, including
the equivariant version. This generalizes the known construction of A-infinity
algebra via summation over ribbon trees. These solutions give naturally the
supersymmetric matrix action functionals, which are the gl(N)-equivariantly
closed differential forms on the matrix spaces, which were introduced in one of
my previous papers "Noncommmutative Batalin-Vilkovisky geometry and Matrix
integrals" (arXiv:0912.5484, electronic CNRS preprint
hal-00102085(28/09/2006)).Comment: 17 pages, electronic CNRS preprint hal-00464794 (17/03/2010
Abelian Duality
We show that on three-dimensional Riemannian manifolds without boundaries and
with trivial first real de Rham cohomology group (and in no other dimensions)
scalar field theory and Maxwell theory are equivalent: the ratio of the
partition functions is given by the Ray-Singer torsion of the manifold. On the
level of interaction with external currents, the equivalence persists provided
there is a fixed relation between the charges and the currents.Comment: 11 pages, LaTeX, no figures, a reference added, submitted to Phys.
Rev.
Addenda and corrections to work done on the path-integral approach to classical mechanics
In this paper we continue the study of the path-integral formulation of
classical mechanics and in particular we better clarify, with respect to
previous papers, the geometrical meaning of the variables entering this
formulation. With respect to the first paper with the same title, we {\it
correct} here the set of transformations for the auxiliary variables
. We prove that under this new set of transformations the
Hamiltonian , appearing in our path-integral, is an exact
scalar and the same for the Lagrangian. Despite this different transformation,
the variables maintain the same operatorial meaning as before but
on a different functional space. Cleared up this point we then show that the
space spanned by the whole set of variables () of our
path-integral is the cotangent bundle to the {\it reversed-parity} tangent
bundle of the phase space of our system and it is indicated as
. In case the reader feel uneasy with this strange
{\it Grassmannian} double bundle, we show in this paper that it is possible to
build a different path-integral made only of {\it bosonic} variables. These
turn out to be the coordinates of which is the
double cotangent bundle of phase-space.Comment: Title changed, appendix expanded, few misprints fixe
Planar sandwich antennas for submillimeter applications
A planar receiving antenna with a predictable pattern at submillimeter wavelength is demonstrated experimentally for the first time. It is single lobed and efficient, with a gain of approximately 8 dB at a wavelength of 119 µm
Kinematic and morphological modeling of the bipolar nebula Sa2-237
We present [OIII]500.7nm and Halpha+[NII] images and long-slit, high
resolution echelle spectra in the same spectral regions of Sa2--237, a possible
bipolar planetary nebula. The image shows a bipolar nebula of about 34" extent,
with a narrow waist, and showing strong point symmetry about the central
object, indicating it's likely binary nature. The long slit spectra were taken
over the long axis of the nebula, and show a distinct ``eight'' shaped pattern
in the velocity--space plot, and a maximum projected outflow velocity of
V=106km/s, both typical of expanding bipolar planetary nebulae. By model
fitting the shape and spectrum of the nebula simultaneously, we derive the
inclination of the long axis to be 70 degrees, and the maximum space velocity
of expansion to be 308 km/s. Due to asymmetries in the velocities we adopt a
new value for the system's heliocentric radial velocity of -30km/s. We use the
IRAS and 21cm radio fluxes, the energy distribution, and the projected size of
Sa2-237 to estimate it's distance to be 2.1+-0.37kpc. At this distance Sa2-237
has a luminosity of 340 Lsun, a size of 0.37pc, and -- assuming constant
expansion velocity -- a nebular age of 624 years. The above radial velocity and
distance place Sa2--237 in the disk of the Galaxy at z=255pc, albeit with
somewhat peculiar kinematics.Comment: 10pp, 4 fig
Effect of Poisson ratio on cellular structure formation
Mechanically active cells in soft media act as force dipoles. The resulting
elastic interactions are long-ranged and favor the formation of strings. We
show analytically that due to screening, the effective interaction between
strings decays exponentially, with a decay length determined only by geometry.
Both for disordered and ordered arrangements of cells, we predict novel phase
transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a
function of Poisson ratio.Comment: 4 pages, Revtex, 4 Postscript figures include
Zeta-Function Regularization is Uniquely Defined and Well
Hawking's zeta function regularization procedure is shown to be rigorously
and uniquely defined, thus putting and end to the spreading lore about
different difficulties associated with it. Basic misconceptions,
misunderstandings and errors which keep appearing in important scientific
journals when dealing with this beautiful regularization method ---and other
analytical procedures--- are clarified and corrected.Comment: 7 pages, LaTeX fil
Type IIB instanton as a wave in twelve dimensions
0-brane of type IIA string theory can be interpreted as a dimensional
reduction of a gravitational wave in 11 dimensions. We observe that a similar
interpretation applies also to the D-instanton background of type IIB theory:
it can be viewed as a reduction (along one spatial and one time-like direction)
of a wave in a 12-dimensional theory. The instanton charge is thus related to a
linear momentum in 12 dimensions. This suggests that the instanton should play
as important role in type IIB theory as the 0-brane is supposed to play in type
IIA theory.Comment: 7 pages, harvmac (minor corrections and a reference added
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