537 research outputs found
Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle
Causal fermion systems are introduced as a general mathematical framework for
formulating relativistic quantum theory. By specializing, we recover earlier
notions like fermion systems in discrete space-time, the fermionic projector
and causal variational principles. We review how an effect of spontaneous
structure formation gives rise to a topology and a causal structure in
space-time. Moreover, we outline how to construct a spin connection and
curvature, leading to a proposal for a "quantum geometry" in the Lorentzian
setting. We review recent numerical and analytical results on the support of
minimizers of causal variational principles which reveal a "quantization
effect" resulting in a discreteness of space-time. A brief survey is given on
the correspondence to quantum field theory and gauge theories.Comment: 23 pages, LaTeX, 2 figures, footnote added on page
A New Proposal for the Picture Changing Operators in the Minimal Pure Spinor Formalism
Using a new proposal for the "picture lowering" operators, we compute the
tree level scattering amplitude in the minimal pure spinor formalism by
performing the integration over the pure spinor space as a multidimensional
Cauchy-type integral. The amplitude will be written in terms of the projective
pure spinor variables, which turns out to be useful to relate rigorously the
minimal and non-minimal versions of the pure spinor formalism. The natural
language for relating these formalisms is the Cech-Dolbeault isomorphism.
Moreover, the Dolbeault cocycle corresponding to the tree-level scattering
amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor
space, which means that the origin is removed from this space. Also, the
Cech-Dolbeault language plays a key role for proving the invariance of the
scattering amplitude under BRST, Lorentz and supersymmetry transformations, as
well as the decoupling of unphysical states. We also relate the Green's
function for the massless scalar field in ten dimensions to the tree-level
scattering amplitude and comment about the scattering amplitude at higher
orders. In contrast with the traditional picture lowering operators, with our
new proposal the tree level scattering amplitude is independent of the constant
spinors introduced to define them and the BRST exact terms decouple without
integrating over these constant spinors.Comment: 56 pages, typos correcte
Particle Kinematics in Horava-Lifshitz Gravity
We study the deformed kinematics of point particles in the Horava theory of
gravity. This is achieved by considering particles as the optical limit of
fields with a generalized Klein-Gordon action. We derive the deformed geodesic
equation and study in detail the cases of flat and spherically symmetric
(Schwarzschild-like) spacetimes. As the theory is not invariant under local
Lorenz transformations, deviations from standard kinematics become evident even
for flat manifolds, supporting superluminal as well as massive luminal
particles. These deviations from standard behavior could be used for
experimental tests of this modified theory of gravity.Comment: Added references, corrected a typing erro
An Efficient Representation of Euclidean Gravity I
We explore how the topology of spacetime fabric is encoded into the local
structure of Riemannian metrics using the gauge theory formulation of Euclidean
gravity. In part I, we provide a rigorous mathematical foundation to prove that
a general Einstein manifold arises as the sum of SU(2)_L Yang-Mills instantons
and SU(2)_R anti-instantons where SU(2)_L and SU(2)_R are normal subgroups of
the four-dimensional Lorentz group Spin(4) = SU(2)_L x SU(2)_R. Our proof
relies only on the general properties in four dimensions: The Lorentz group
Spin(4) is isomorphic to SU(2)_L x SU(2)_R and the six-dimensional vector space
of two-forms splits canonically into the sum of three-dimensional vector spaces
of self-dual and anti-self-dual two-forms. Consolidating these two, it turns
out that the splitting of Spin(4) is deeply correlated with the decomposition
of two-forms on four-manifold which occupies a central position in the theory
of four-manifolds.Comment: 31 pages, 1 figur
Safety and feasibility of switching from phenytoin to levetiracetam monotherapy for glioma-related seizure control following craniotomy: a randomized phase II pilot study
Seizures are common in patients with gliomas, and phenytoin (PHT) is frequently used to control tumor-related seizures. PHT, however, has many undesirable side effects (SEs) and drug interactions with glioma chemotherapy. Levetiracetam (LEV) is a newer antiepileptic drug (AED) with fewer SEs and essentially no drug interactions. We performed a pilot study testing the safety and feasibility of switching patients from PHT to LEV monotherapy for postoperative control of glioma-related seizures. Over a 13-month period, 29 patients were randomized in a 2:1 ratio to initiate LEV therapy within 24 h of surgery or to continue PHT therapy. 6 month follow-up data were available for 15 patients taking LEV and for 8 patients taking PHT. In the LEV group, 13 patients (87%) were seizure-free. In the PHT group, 6 patients (75%) were seizure-free. Reported SEs at 6 months was as follows (%LEV/%PHT group): dizziness (0/14), difficulty with coordination (0/29), depression (7/14) lack of energy or strength (20/43), insomnia (40/43), mood instability (7/0). The pilot data presented here suggest that it is safe to switch patients from PHT to LEV monotherapy following craniotomy for supratentorial glioma. A large-scale, double-blinded, randomized control trial of LEV versus PHT is required to determine seizure control equivalence and better assess differences in SEs
Discrete conformal maps: boundary value problems, circle domains, Fuchsian and Schottky uniformization
We discuss several extensions and applications of the theory of discretely conformally equivalent triangle meshes (two meshes are considered conformally equivalent if corresponding edge lengths are related by scale factors attached to the vertices). We extend the fundamental definitions and variational principles from triangulations to polyhedral surfaces with cyclic faces. The case of quadrilateral meshes is equivalent to the cross ratio system, which provides a link to the theory of integrable systems. The extension to cyclic polygons also brings discrete conformal maps to circle domains within the scope of the theory. We provide results of numerical experiments suggesting that discrete conformal maps converge to smooth conformal maps, with convergence rates depending on the mesh quality. We consider the Fuchsian uniformization of Riemann surfaces represented in different forms: as immersed surfaces in \mathbb {R}^{3}, as hyperelliptic curves, and as \mathbb {CP}^{1} modulo a classical Schottky group, i.e., we convert Schottky to Fuchsian uniformization. Extended examples also demonstrate a geometric characterization of hyperelliptic surfaces due to Schmutz Schaller
Recommended from our members
Cosmogenic neutron production at the Sudbury Neutrino Observatory
Neutrons produced in nuclear interactions initiated by cosmic-ray muons present an irreducible background to many rare-event searches, even in detectors located deep underground. Models for the production of these neutrons have been tested against previous experimental data, but the extrapolation to deeper sites is not well understood. Here we report results from an analysis of cosmogenically produced neutrons at the Sudbury Neutrino Observatory. A specific set of observables are presented, which can be used to benchmark the validity of geant4 physics models. In addition, the cosmogenic neutron yield, in units of 10-4 cm2/(g·μ), is measured to be 7.28±0.09(stat)-1.12+1.59(syst) in pure heavy water and 7.30±0.07(stat)-1.02+1.40(syst) in NaCl-loaded heavy water. These results provide unique insights into this potential background source for experiments at SNOLAB
Constraints on Nucleon Decay via "Invisible" Modes from the Sudbury Neutrino Observatory
Data from the Sudbury Neutrino Observatory have been used to constrain the
lifetime for nucleon decay to ``invisible'' modes, such as n -> 3 nu. The
analysis was based on a search for gamma-rays from the de-excitation of the
residual nucleus that would result from the disappearance of either a proton or
neutron from O16. A limit of tau_inv > 2 x 10^{29} years is obtained at 90%
confidence for either neutron or proton decay modes. This is about an order of
magnitude more stringent than previous constraints on invisible proton decay
modes and 400 times more stringent than similar neutron modes.Comment: Update includes missing efficiency factor (limits change by factor of
2) Submitted to Physical Review Letter
First Neutrino Observations from the Sudbury Neutrino Observatory
The first neutrino observations from the Sudbury Neutrino Observatory are
presented from preliminary analyses. Based on energy, direction and location,
the data in the region of interest appear to be dominated by 8B solar
neutrinos, detected by the charged current reaction on deuterium and elastic
scattering from electrons, with very little background. Measurements of
radioactive backgrounds indicate that the measurement of all active neutrino
types via the neutral current reaction on deuterium will be possible with small
systematic uncertainties. Quantitative results for the fluxes observed with
these reactions will be provided when further calibrations have been completed.Comment: Latex, 7 pages, 10 figures, Invited paper at Neutrino 2000
Conference, Sudbury, Canada, June 16-21, 2000 to be published in the
Proceeding
- …