63 research outputs found
Discrete Quantum Field Theories and the Intersection Form
It is shown that the standard mod- valued intersection form can be used to
define Boltzmann weights of subdivision invariant lattice models with gauge
group . In particular, we discuss a four dimensional model which is
based upon the assignment of field variables to the -simplices of the
simplicial complex. The action is taken to be the intersection form defined on
the second cohomology group of the complex, with coefficients in .
Subdivision invariance of the theory follows when the coupling constant is
quantized and the field configurations are restricted to those satisfying a
mod- flatness condition. We present an explicit computation of the partition
function for the manifold , demonstrating non-triviality.Comment: 10 pages, Latex, ITFA-94-1
String Motion on SDiff(M) and Hydrodynamics with Internal Degrees of Freedom
We consider classical string theory where the target space SDiff(M) is the infinite dimensional group of volume preserving diffeomorphisms of a smooth manifold M. In analogy with the case of free point particle motion on SDiff(M), where the geodesic equation is equivalent to the Euler equation for an incompressible fluid, we find a new set of coupled nonlinear equations. These can be interpreted as equations for a perfect fluid with some internal degrees of freedom. Some subtleties involved in quantizing this geometrical picture are discussed
On the Quantum Kinetic Equation in Weak Turbulence
The quantum kinetic equation used in the study of weak turbulence is
reconsidered in the context of a theory with a generic quartic interaction. The
expectation value of the time derivative of the mode number operators is
computed in a perturbation expansion which places the large diagonal component
of the quartic term in the unperturbed Hamiltonian. Although one is not
perturbing around a free field theory, the calculation is easily tractable
owing to the fact that the unperturbed Hamiltonian can be written solely in
terms of the mode number operators.Comment: 12 pages, LATEX, no figures, to appear in Phys. Rev.
Topological Modes in Dual Lattice Models
Lattice gauge theory with gauge group is reconsidered in four
dimensions on a simplicial complex . One finds that the dual theory,
formulated on the dual block complex , contains topological modes
which are in correspondence with the cohomology group ,
in addition to the usual dynamical link variables. This is a general phenomenon
in all models with single plaquette based actions; the action of the dual
theory becomes twisted with a field representing the above cohomology class. A
similar observation is made about the dual version of the three dimensional
Ising model. The importance of distinct topological sectors is confirmed
numerically in the two dimensional Ising model where they are parameterized by
.Comment: 10 pages, DIAS 94-3
On Dijkgraaf-Witten Type Invariants
We explicitly construct a series of lattice models based upon the gauge group
which have the property of subdivision invariance, when the coupling
parameter is quantized and the field configurations are restricted to satisfy a
type of mod- flatness condition. The simplest model of this type yields the
Dijkgraaf-Witten invariant of a -manifold and is based upon a single link,
or -simplex, field. Depending upon the manifold's dimension, other models
may have more than one species of field variable, and these may be based on
higher dimensional simplices.Comment: 18 page
State Sum Models and Simplicial Cohomology
We study a class of subdivision invariant lattice models based on the gauge
group , with particular emphasis on the four dimensional example. This
model is based upon the assignment of field variables to both the - and
-dimensional simplices of the simplicial complex. The property of
subdivision invariance is achieved when the coupling parameter is quantized and
the field configurations are restricted to satisfy a type of mod- flatness
condition. By explicit computation of the partition function for the manifold
, we establish that the theory has a quantum Hilbert space
which differs from the classical one.Comment: 28 pages, Latex, ITFA-94-13, (Expanded version with two new sections
Exploiting Laboratory and Heliophysics Plasma Synergies
Recent advances in space-based heliospheric observations, laboratory experimentation, and plasma simulation codes are creating an exciting new cross-disciplinary opportunity for understanding fast energy release and transport mechanisms in heliophysics and laboratory plasma dynamics, which had not been previously accessible. This article provides an overview of some new observational, experimental, and computational assets, and discusses current and near-term activities towards exploitation of synergies involving those assets. This overview does not claim to be comprehensive, but instead covers mainly activities closely associated with the authorsâ interests and reearch. Heliospheric observations reviewed include the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) on the National Aeronautics and Space Administration (NASA) Solar Terrestrial Relations Observatory (STEREO) mission, the first instrument to provide remote sensing imagery observations with spatial continuity extending from the Sun to the Earth, and the Extreme-ultraviolet Imaging Spectrometer (EIS) on the Japanese Hinode spacecraft that is measuring spectroscopically physical parameters of the solar atmosphere towards obtaining plasma temperatures, densities, and mass motions. The Solar Dynamics Observatory (SDO) and the upcoming Solar Orbiter with the Heliospheric Imager (SoloHI) on-board will also be discussed. Laboratory plasma experiments surveyed include the line-tied magnetic reconnection experiments at University of Wisconsin (relevant to coronal heating magnetic flux tube observations and simulations), and a dynamo facility under construction there; the Space Plasma Simulation Chamber at the Naval Research Laboratory that currently produces plasmas scalable to ionospheric and magnetospheric conditions and in the future also will be suited to study the physics of the solar corona; the Versatile Toroidal Facility at the Massachusetts Institute of Technology that provides direct experimental observation of reconnection dynamics; and the Swarthmore Spheromak Experiment, which provides well-diagnosed data on three-dimensional (3D) null-point magnetic reconnection that is also applicable to solar active regions embedded in pre-existing coronal fields. New computer capabilities highlighted include: HYPERION, a fully compressible 3D magnetohydrodynamics (MHD) code with radiation transport and thermal conduction; ORBIT-RF, a 4D Monte-Carlo code for the study of wave interactions with fast ions embedded in background MHD plasmas; the 3D implicit multi-fluid MHD spectral element code, HiFi; and, the 3D Hall MHD code VooDoo. Research synergies for these new tools are primarily in the areas of magnetic reconnection, plasma charged particle acceleration, plasma wave propagation and turbulence in a diverging magnetic field, plasma atomic processes, and magnetic dynamo behavior.United States. Office of Naval ResearchNaval Research Laboratory (U.S.
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