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

Chaos-Order Transition in Matrix Theory

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.Comment: 14 pages, Latex, 10 figure

Analysis of scalar perturbations in cosmological models with a non-local scalar field

We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex.Comment: LaTeX, 25 pages, 1 figure, v2: Subsection 3.2 and Section 5 added, references added, accepted for publication in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:0903.517

Quantization of the Riemann Zeta-Function and Cosmology

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories. This approach is motivated by the theory of p-adic strings and by recent works on stringy cosmological models. We show that the Lagrangian for the zeta-function field is equivalent to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and the Langlands program is indicated. The Beilinson conjectures on the values of L-functions of motives are interpreted as dealing with the cosmological constant problem. Possible cosmological applications of the zeta-function field theory are discussed.Comment: 14 pages, corrected typos, references and comments adde

Localization of the SFT inspired Nonlocal Linear Models and Exact Solutions

A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function $F(\Box)$, which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented.Comment: 20 pages, 3 figures, published in the proceedings of the VIII International Workshop "Supersymmetries and Quantum Symmetries" (SQS'09), Dubna, Russia, July 29 - August 3, 2009, http://theor.jinr.ru/~sqs09

Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric

A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.Comment: 18 pages, 3 figures, a few misprints in Section 5 have been correcte

Reconstructing Images from Projections Using the Maximum-Entropy Method. Numerical Simulations of Low-Aspect Astrotomography

The reconstruction of images from a small number of projections using the maximum-entropy method (MEM) with the Shannon entropy is considered. MEM provides higher-quality image reconstruction for sources with extended components than the Hogbom CLEAN method, which is also used in low-aspect astrotomography. The quality of image reconstruction for sources with mixed structure containing bright, compact features embedded in a comparatively weak, extended base can be further improved using a difference-mapping method, which requires a generalization of MEM for the reconstruction of sign-variable functions.We draw conclusions based on the results of numerical simulations for a number of model radio sources with various morphologies.Comment: 11 pages, 9 figure

Non-minimally Coupled Cosmological Models with the Higgs-like Potentials and Negative Cosmological Constant

We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Universe evolution with oscillation behaviour of the Hubble parameter from positive to negative values. Depending on the initial conditions the Hubble parameter can perform either one or several cycles before to become negative forever.Comment: 22 pages, 6 figures, v4:Section 2 expanded, references added, accepted for publication in Class. Quant. Gra

Variations of Infinite Derivative Modified Gravity

We consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form $P(R) F(\Box) Q(R)$. For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein-Hilbert modified action and basics of gravity perturbations.Comment: 22 page

Crossing the Phantom Divide Line in a DGP-Inspired F(R,ϕ)F(R,\phi)-Gravity

We study possible crossing of the phantom divide line in a DGP-inspired $F(R,\phi)$ braneworld scenario where scalar field and curvature quintessence are treated in a unified framework. With some specific form of $F(R,\phi)$ and by adopting a suitable ansatz, we show that there are appropriate regions of the parameters space which account for late-time acceleration and admit crossing of the phantom divide line.Comment: 23 Pages, 10 figs, Submitted to JCA