Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, ``comma'' and matrix representations of vertices.Comment: 160 pages, LaTeX, 29 EPS figures. Lectures given by I.Ya.Aref'eva at the Swieca Summer School, Brazil, January 2001; Summer School in Modern Mathematical Physics, Sokobanja, Yugoslavia, August 2001; Max Born Symposium, Karpacz, Poland, September, 2001; Workshop "Noncommutative Geometry, Strings and Renormalization", Leipzig, Germany, September 2001. Typos corrected, references adde

Pisgah Lava Cave Communication Test: Science Case Study for the Networked Constellations Initiative

As part of the science case study for the Networked Constellations initiative, a team of JPL scientists explore the possibility of a mission to study the lava caves on Mars. Natural caves on Mars and the Moon present a unique opportunity to learn about the planetary geology and to provide a shelter for human explorers. Due to power and communication challenges, a network of assets has significant advantages over a single asset sent inside a cave. However, communication between the assets and the data downlink present significant difficulties due to the presence of rough walls, boulders, and other obstacles with unknown dielectric constant inside a typical cave, disturbing the propagation of the radio waves. A detailed study is needed to establish the limitations of the current communication technologies and to develop requirements for the new communication technology applicable to the cave environment. On May 4 of 2017, Konstantin Belov, Doug Ellison, and Abby Fraeman visited a lava cave in Pisgah, CA. The purpose of the visit was to build a 3D map of the cave, which could be used to create a model of radio wave propagation, and to conduct a series of communication tests using off-the-shelf equipment to verify the in-cave communication challenges. This experiment should be considered as a simple 'proof of concept' and is the subject of this report

Sub-wavelength imaging at infrared frequencies using an array of metallic nanorods

We demonstrate that an array of metallic nanorods enables sub-wavelength (near-field) imaging at infrared frequencies. Using an homogenization approach, it is theoretically proved that under certain conditions the incoming radiation can be transmitted by the array of nanorods over a significant distance with fairly low attenuation. The propagation mechanism does not involve a resonance of material parameters and thus the resolution is not strongly affected by material losses and has wide bandwidth. The sub-wavelength imaging with $\lambda/10$ resolution by silver rods at 30 THz is demonstrated numerically using full-wave electromagnetic simulator.Comment: 12 pages, 16 figures, submitted to PR

The evolution operator of the Hartree-type equation with a quadratic potential

Based on the ideology of the Maslov's complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. The nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.Comment: 23 pege

Lattice analogues of W-algebras and Classical Integrable Equations

We propose a regular way to construct lattice versions of $W$-algebras, both for quantum and classical cases. In the classical case we write the algebra explicitly and derive the lattice analogue of Boussinesq equation from the Hamiltonian equations of motion. Connection between the lattice Faddeev-Takhtadjan-Volkov algebra [1] and q-deformed Virasoro is also discussed.Comment: LaTeX, ILG-TMP-93-01, (the problems caused by mailer are fixed