Gauge Dressing of 2D Field Theories

By using the gauge Ward identities, we study correlation functions of gauged WZNW models. We show that the gauge dressing of the correlation functions can be taken into account as a solution of the Knizhnik-Zamolodchikov equation. Our method is analogous to the analysis of the gravitational dressing of 2D field theories.Comment: 13 pages, Late

Two classes of generalized functions used in nonlocal field theory

We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space $S^0$ (which is the Fourier transform of the Schwartz space $\mathcal D$) and using test functions in the Gelfand-Shilov spaces $S^0_\alpha$. We prove that every functional defined on $S^0$ has the same carrier cones as its restrictions to the smaller spaces $S^0_\alpha$. As an application of this result, we derive a Paley-Wiener-Schwartz-type theorem for arbitrarily singular generalized functions of tempered growth and obtain the corresponding extension of Vladimirov's algebra of functions holomorphic on a tubular domain.Comment: AMS-LaTeX, 12 pages, no figure

Axiomatic formulations of nonlocal and noncommutative field theories

We analyze functional analytic aspects of axiomatic formulations of nonlocal and noncommutative quantum field theories. In particular, we completely clarify the relation between the asymptotic commutativity condition, which ensures the CPT symmetry and the standard spin-statistics relation for nonlocal fields, and the regularity properties of the retarded Green's functions in momentum space that are required for constructing a scattering theory and deriving reduction formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem for analytic functionals. We also discuss the possibility of using analytic test functions to extend the Wightman axioms to noncommutative field theory, where the causal structure with the light cone is replaced by that with the light wedge. We explain some essential peculiarities of deriving the CPT and spin-statistics theorems in this enlarged framework.Comment: LaTeX, 13 pages, no figure

Towards a Generalized Distribution Formalism for Gauge Quantum Fields

We prove that the distributions defined on the Gelfand-Shilov spaces, and hence more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables one to develop a distribution-theoretic techniques suitable for the consistent treatment of quantum fields with arbitrarily singular ultraviolet and infrared behavior. The proofs covering the most general case are based on the use of the theory of plurisubharmonic functions and Hormander's estimates.Comment: 12 p., Department of Theoretical Physics, P.N.Lebedev Physical Institute, Leninsky prosp. 53, Moscow 117924, Russi

Twisted convolution and Moyal star product of generalized functions

We consider nuclear function spaces on which the Weyl-Heisenberg group acts continuously and study the basic properties of the twisted convolution product of the functions with the dual space elements. The final theorem characterizes the corresponding algebra of convolution multipliers and shows that it contains all sufficiently rapidly decreasing functionals in the dual space. Consequently, we obtain a general description of the Moyal multiplier algebra of the Fourier-transformed space. The results extend the Weyl symbol calculus beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure

Superconducting Phase Domains for Memory Applications

In this work we study theoretically the properties of S-F/N-sIS type Josephson junctions in the frame of the quasiclassical Usadel formalism. The structure consists of two superconducting electrodes (S), a tunnel barrier (I), a combined normal metal/ferromagnet (N/F) interlayer and a thin superconducting film (s). We demonstrate the breakdown of a spatial uniformity of the superconducting order in the s-film and its decomposition into domains with a phase shift $\pi$ . The effect is sensitive to the thickness of the s layer and the widths of the F and N films in the direction along the sIS interface. We predict the existence of a regime where the structure has two energy minima and can be switched between them by an electric current injected laterally into the structure. The state of the system can be non-destructively read by an electric current flowing across the junction

Josephson effect in SIFS-tunnel junctions with domain walls in weak link region

We study theoretically the properties of SIFS type Josephson junctions composed of two superconducting (S) electrodes separated by an insulating layer (I) and a ferromagnetic (F) film consisting of periodic magnetic domains structure with antiparallel magnetization directions in neighboring domains. The two-dimensional problem in the weak link area is solved analytically in the framework of the linearized quasiclassical Usadel equations. Based on this solution, the spatial distributions of the critical current density, $J_{C},$ in the domains and critical current, $I_{C},$ of SIFS structures are calculated as a function of domain wall parameters, as well as the thickness, $d_{F},$ and the width, $W,$ of the domains. We demonstrate that $I_{C}(d_{F},W)$ dependencies exhibit damped oscillations with the ratio of the decay length, $\xi_{1},$ and oscillation period, $\xi_{2},$ being a function of the parameters of the domains, and this ratio may take any value from zero to unity. Thus, we propose a new physical mechanism that may explain the essential difference between $\xi_{1}$ and $\xi_{2}$ observed experimentally in various types of SFS Josephson junctions.Comment: The paper will be published in JETP letters vol 101, issue 11, 201