Non-commutative deformation of Chern-Simons theory

The problem of the consistent definition of gauge theories living on the non-commutative (NC) spaces with a non-constant NC parameter $\Theta(x)$ is discussed. Working in the L$_\infty$ formalism we specify the undeformed theory, $3$d abelian Chern-Simons, by setting the initial $\ell_1$ brackets. The deformation is introduced by assigning the star commutator to the $\ell_2$ bracket. For this initial set up we construct the corresponding L$_\infty$ structure which defines both the NC deformation of the abelian gauge transformations and the field equations covariant under these transformations. To compensate the violation of the Leibniz rule one needs the higher brackets which are proportional to the derivatives of $\Theta$. Proceeding in the slowly varying field approximation when the star commutator is approximated by the Poisson bracket we derive the recurrence relations for the definition of these brackets for arbitrary $\Theta$. For the particular case of $su(2)$-like NC space we obtain an explicit all orders formulas for both NC gauge transformations and NC deformation of Chern-Simons equations. The latter are non-Lagrangian and are satisfied if the NC field strength vanishes everywhere.Comment: 33 pages, published version, exposition improved, new material regarding the definition of the non-commutative field strength and the treatment of the non-commutativity of general form adde

Systematic approach to nonlinear filtering associated with aggregation operators. Part 1. SISO-filters

There are various methods to help restore an image from noisy distortions. Each technique has its advantages and disadvantages. Selecting the appropriate method plays a major role in getting the desired image. Noise removal or noise reduction can be done on an image by linear or nonlinear filtering. The more popular linear technique is based on average (on mean) linear operators. Denoising via linear filters normally does not perform satisfactorily since both noise and edges contain high frequencies. Therefore, any practical denoising model has to be nonlinear. In this work, we introduce and analyze a new class of nonlinear SISO-filters that have their roots in aggregation operator theory. We show that a large body of non-linear filters proposed to date constitute a proper subset of aggregation filters. (C) 2017 The Authors. Published by Elsevier Ltd.This work was supported by grants the RFBR No. 17-07-00886 and by Ural State Forest Engineering's Center of Excellence in "Quantum and Classical Information Technologies for Remote Sensing Systems"

Lorentz and CPT Violation in Scalar-Mediated Potentials

In Lorentz- and CPT-violating effective field theories involving scalar and spinor fields, there exist forms of Lorentz violation that modify only the scalar-spinor Yukawa interaction vertices. These affect low-energy fermion and antifermion scattering processes through modifications to the nonrelativistic Yukawa potentials. The modified potentials involve novel combinations of momentum, spin, and Lorentz-violating background tensors.Comment: 16 page

All order covariant tubular expansion

We consider tubular neighborhood of an arbitrary submanifold embedded in a (pseudo-)Riemannian manifold. This can be described by Fermi normal coordinates (FNC) satisfying certain conditions as described by Florides and Synge in \cite{FS}. By generalizing the work of Muller {\it et al} in \cite{muller} on Riemann normal coordinate expansion, we derive all order FNC expansion of vielbein in this neighborhood with closed form expressions for the curvature expansion coefficients. Our result is shown to be consistent with certain integral theorem for the metric proved in \cite{FS}.Comment: 27 pages. Corrected an error in a class of coefficients resulting from a typo. Integral theorem and all other results remain unchange

Supercritical geometric optics for nonlinear Schrodinger equations

We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To overcome this issue, we introduce new unknown functions, which are defined nonlinearly in terms of the wave function itself. This approach provides a local version of the modulated energy functional introduced by Y.Brenier. The system we obtain is hyperbolic symmetric, and the justification of WKB analysis follows.Comment: 29 pages. Some typos fixe