10,116 research outputs found
Duality Symmetries and Noncommutative Geometry of String Spacetime
We examine the structure of spacetime symmetries of toroidally compactified
string theory within the framework of noncommutative geometry. Following a
proposal of Frohlich and Gawedzki, we describe the noncommutative string
spacetime using a detailed algebraic construction of the vertex operator
algebra. We show that the spacetime duality and discrete worldsheet symmetries
of the string theory are a consequence of the existence of two independent
Dirac operators, arising from the chiral structure of the conformal field
theory. We demonstrate that these Dirac operators are also responsible for the
emergence of ordinary classical spacetime as a low-energy limit of the string
spacetime, and from this we establish a relationship between T-duality and
changes of spin structure of the target space manifold. We study the
automorphism group of the vertex operator algebra and show that spacetime
duality is naturally a gauge symmetry in this formalism. We show that classical
general covariance also becomes a gauge symmetry of the string spacetime. We
explore some larger symmetries of the algebra in the context of a universal
gauge group for string theory, and connect these symmetry groups with some of
the algebraic structures which arise in the mathematical theory of vertex
operator algebras, such as the Monster group. We also briefly describe how the
classical topology of spacetime is modified by the string theory, and calculate
the cohomology groups of the noncommutative spacetime. A self-contained,
pedagogical introduction to the techniques of noncommmutative geometry is also
included.Comment: 70 pages, Latex, No Figures. Typos and references corrected. Version
to appear in Communications in Mathematical Physic
Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions
We show that noncommutative gauge theory in two dimensions is an exactly
solvable model. A cohomological formulation of gauge theory defined on the
noncommutative torus is used to show that its quantum partition function can be
written as a sum over contributions from classical solutions. We derive an
explicit formula for the partition function of Yang-Mills theory defined on a
projective module for arbitrary noncommutativity parameter \theta which is
manifestly invariant under gauge Morita equivalence. The energy observables are
shown to be smooth functions of \theta. The construction of noncommutative
instanton contributions to the path integral is described in some detail. In
general, there are infinitely many gauge inequivalent contributions of fixed
topological charge, along with a finite number of quantum fluctuations about
each instanton. The associated moduli spaces are combinations of symmetric
products of an ordinary two-torus whose orbifold singularities are not resolved
by noncommutativity. In particular, the weak coupling limit of the gauge theory
is independent of \theta and computes the symplectic volume of the moduli space
of constant curvature connections on the noncommutative torus.Comment: 52 pages LaTeX, 1 eps figure, uses espf. V2: References added and
repaired; V3: Typos corrected, some clarifying explanations added; version to
be published in Communications in Mathematical Physic
Implications of Particle Acceleration in Active Galactic Nuclei for Cosmic Rays and High Energy Neutrino Astronomy
We consider the production of high energy neutrinos and cosmic rays in
radio-quiet active galactic nuclei (AGN) or in the central regions of
radio-loud AGN. We use a model in which acceleration of protons takes place at
a shock in an accretion flow onto a supermassive black hole, and follow the
cascade that results from interactions of the accelerated protons in the AGN
environment. We use our results to estimate the diffuse high energy neutrino
intensity and cosmic ray intensity due to AGN. We discuss our results in the
context of high energy neutrino telescopes under construction, and measurements
of the cosmic ray composition in the region of the ``knee'' in the energy
spectrum at GeV.Comment: 37 pages of compressed and uuencoded postscript; hardcopy available
on request; to be published in Astroparticle Physics; ADP-AT-94-
String Geometry and the Noncommutative Torus
We construct a new gauge theory on a pair of d-dimensional noncommutative
tori. The latter comes from an intimate relationship between the noncommutative
geometry associated with a lattice vertex operator algebra A and the
noncommutative torus. We show that the (truncated) tachyon subalgebra of A is
naturally isomorphic to a class of twisted modules representing quantum
deformations of the algebra of functions on the torus. We construct the
corresponding even real spectral triples and determine their Morita equivalence
classes using string duality arguments. These constructions yield simple proofs
of the O(d,d;Z) Morita equivalences between -dimensional noncommutative tori
and give a natural physical interpretation of them in terms of the target space
duality group of toroidally compactified string theory. We classify the
automorphisms of the twisted modules and construct the most general gauge
theory which is invariant under the automorphism group. We compute bosonic and
fermionic actions associated with these gauge theories and show that they are
explicitly duality-symmetric. The duality-invariant gauge theory is manifestly
covariant but contains highly non-local interactions. We show that it also
admits a new sort of particle-antiparticle duality which enables the
construction of instanton field configurations in any dimension. The duality
non-symmetric on-shell projection of the field theory is shown to coincide with
the standard non-abelian Yang-Mills gauge theory minimally coupled to massive
Dirac fermion fields.Comment: 37 pages, LaTeX. Major revisions in section 3. Other minor revisions
in the rest of the paper, references adde
Noncommutative theories and general coordinate transformations
We study the class of noncommutative theories in dimensions whose spatial
coordinates can be obtained by performing a smooth change of
variables on , the coordinates of a standard noncommutative
theory, which satisfy the relation , with a
constant tensor. The variables verify a commutation
relation which is, in general, space-dependent. We study the main properties of
this special kind of noncommutative theory and show explicitly that, in two
dimensions, any theory with a space-dependent commutation relation can be
mapped to another where that is constant.Comment: 21 pages, no figures, LaTeX. v2: section 5 added, typos corrected.
Version to appear in Physical Review
An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis
The accurate but expensive product of geminals ansatz may be approximated by
a geminal power, but this approach sacrifices size consistency. Here we show
both analytically and numerically that a size consistent form very similar to
the product of geminals can be recovered using a network of location specific
Jastrow factors. Upon variational energy minimization, the network creates
particle number projections that remove the charge fluctuations responsible for
size inconsistency. This polynomial cost approach captures strong many-electron
correlations, giving a maximum error of just 1.8 kcal/mol during the
double-bond dissociation of H2O in an STO-3G atomic orbital basis.Comment: Updated the original arXiv submission to include improvements
resulting from journal peer review. 5 pages, 4 figures, 1 tabl
Exact Solution of Noncommutative Field Theory in Background Magnetic Fields
We obtain the exact non-perturbative solution of a scalar field theory
defined on a space with noncommuting position and momentum coordinates. The
model describes non-locally interacting charged particles in a background
magnetic field. It is an exactly solvable quantum field theory which has
non-trivial interactions only when it is defined with a finite ultraviolet
cutoff. We propose that small perturbations of this theory can produce solvable
models with renormalizable interactions.Comment: 9 Pages AMSTeX; Typos correcte
Motion Capture System for Finger Movement Measurement in Parkinson Disease
Parkinson’s disease (PD) is a chronic neurodegenerative disorder that affects almost 1% of the population in the age group above 60 years. The key symptom in PD is the restriction of mobility. The progress of PD is typically documented using the Unified Parkinson’s Disease Rating Scale (UPDRS), which includes a finger-tapping test. We created a measurement tool and a methodology for the objective measurement of the finger-tapping test. We built a contactless three-dimensional (3D) capture system using two cameras and light-passive (wireless) reflexive markers. We proposed and implemented an algorithm for extracting, matching, and tracing markers. The system provides the 3D position of spherical or hemispherical markers in real time. The system’s functionality was verified with the commercial motion capture system OptiTrack. Our motion capture system is easy to use, saves space, is transportable, and needs only a personal computer for data processing—the ideal solution for an outpatient clinic. Its features were successfully tested on 22 patients with PD and 22 healthy control subjects
Induced Dilaton in Topologically Massive Quantum Field Theory
We consider the conformally-invariant coupling of topologically massive
gravity to a dynamical massless scalar field theory on a three-manifold with
boundary. We show that, in the phase of spontaneously broken Lorentz and Weyl
symmetries, this theory induces the target space zero mode of the vertex
operator for the string dilaton field on the boundary of the three-dimensional
manifold. By a further coupling to topologically massive gauge fields in the
bulk, we demonstrate directly from the three-dimensional theory that this
dilaton field transforms in the expected way under duality transformations so
as to preserve the mass gaps in the spectra of the gauge and gravitational
sectors of the quantum field theory. We show that this implies an intimate
dynamical relationship between T-duality and S-duality transformations of the
quantum string theory. The dilaton in this model couples bulk and worldsheet
degrees of freedom to each other and generates a dynamical string coupling.Comment: 26 pages RevTeX, 1 figure, uses epsf.st
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