(1+1)-Dimensional Yang-Mills Theory Coupled to Adjoint Fermions on the Light Front

We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)/Z_2, which possesses nontrivial topology. In particular, there are two distinct topological sectors and the physical vacuum state has a structure analogous to a \theta vacuum. We show how this feature is realized in light-front quantization, with periodicity conditions used to regulate the infrared and treating the gauge field zero mode as a dynamical quantity. We find expressions for the degenerate vacuum states and construct the analog of the \theta vacuum. We then calculate the bilinear condensate in the model. We argue that the condensate does not affect the spectrum of the theory, although it is related to the string tension that characterizes the potential between fundamental test charges when the dynamical fermions are given a mass. We also argue that this result is fundamentally different from calculations that use periodicity conditions in x^1 as an infrared regulator.Comment: 20 pages, Revte

Renormalization of Tamm-Dancoff Integral Equations

During the last few years, interest has arisen in using light-front Tamm-Dancoff field theory to describe relativistic bound states for theories such as QCD. Unfortunately, difficult renormalization problems stand in the way. We introduce a general, non-perturbative approach to renormalization that is well suited for the ultraviolet and, presumably, the infrared divergences found in these systems. We reexpress the renormalization problem in terms of a set of coupled inhomogeneous integral equations, the ``counterterm equation.'' The solution of this equation provides a kernel for the Tamm-Dancoff integral equations which generates states that are independent of any cutoffs. We also introduce a Rayleigh-Ritz approach to numerical solution of the counterterm equation. Using our approach to renormalization, we examine several ultraviolet divergent models. Finally, we use the Rayleigh-Ritz approach to find the counterterms in terms of allowed operators of a theory.Comment: 19 pages, OHSTPY-HEP-T-92-01

Non-Perturbative Spectrum of Two Dimensional (1,1) Super Yang-Mills at Finite and Large N

We consider the dimensional reduction of N = 1 SYM_{2+1} to 1+1 dimensions, which has (1,1) supersymmetry. The gauge groups we consider are U(N) and SU(N), where N is a finite variable. We implement Discrete Light-Cone Quantization to determine non-perturbatively the bound states in this theory. A careful analysis of the spectrum is performed at various values of N, including the case where N is large (but finite), allowing a precise measurement of the 1/N effects in the quantum theory. The low energy sector of the theory is shown to be dominated by string-like states. The techniques developed here may be applied to any two dimensional field theory with or without supersymmetry.Comment: LaTex 18 pages; 5 Encapsulated PostScript figure

ПОКАЗНИКИ ГЕМОПОЕЗУ СОБАК ЗА БАБЕЗІОЗУ

The article presents the results of research on the state of hematopoiesis dogs acute babesiosis course. It was found that for the destruction of red blood cells Babesia canis in the development of the disease develops regenerative, macrocytic anemia, accompanied olihotsytemiyeyu, olihohromemiyeyu, macrocytosis reticulocytosis, thrombocytopenia, increased ESR. This reduction in the number of red blood cells prevailed over reduction of hemoglobin, which suggests a hemolytic process.Already in the early stages of the disease is detected the presence of poikilocytosis ehinotsytiv, akantotsytiv and stomatotsytiv. In the third stage of the disease in the bloodstream appear fragments of erythrocytes (shyzotsyty) and their basophilic stippling.Evidence of the high requirement of oxygen by hemolysis is confirmed by the increasing number of reticulocytes, which strongly leached from bone marrow into peripheral blood.Reducing the number of platelets in the blood flow of dogs for acute babesiosis is strengthened by their destruction and reduction of production due to splenomegaly due to sequestration (deposit) of these blood cells.For babesiosis in dogs develop metabolic ferumovmistymyh pigments (hemochromatosis), confirmed hipersyderemiyeyu and may indicate a postponement of iron in the liver, kidneys and muscles.В статье представлены результаты исследований состояния гемопоэза собак при остром течении бабезиоза. Установлено, что при разрушении эритроцитов Babesia canis в процессе развития заболевания развивается регенераторно-макроцитарная анемия, что сопровождается олигоцитемией, олигохромемией, макроцитозом, ретикулоцитозом, тромбоцитопенией, повышением СОЭ. При этом уменьшение количества эритроцитов преобладало над снижением содержания гемоглобина, что и дает основания считать такой процесс гемолитическим.Уже на первых этапах развития болезни диагностируется пойкилоцитоз с наличием ехиноцитов, акантоцитов и стоматоцитов. В третьей стадии болезни в русле крови появлялись отрывки эритроцитов (шизоциты) и их базофильная зернистость. Свидетельство о высокой потребности организма в кислороде при гемолизе подтверждается растущим количеством ретикулоцитов, что усиленно вымываются из костного мозга в периферическую кровь.Снижение количества тромбоцитов в крови собак при остром течении бабезиоза происходит при усиленном их разрушении и уменьшении продукции вследствии спленомегалии за счет секвестрации (депонирования) этих клеток крови.При бабезиозе у собак развивается нарушение обмена ферумвместимих пигментов (гемохроматоз), что подтверждается гиперсидеремией и может свидетельствовать об отложении железа в печени, почках, мышцах.У статті подані результати досліджень стану гемопоезу собак за гострого перебігу бабезіозу. З’ясовано, що за руйнування еритроцитів Babesia canis в процесі розвитку захворювання розвивається регенераторно-макроцитарна анемія, що супроводжується олігоцитемією, олігохромемією, макроцитозом, ретикулоцитозом, тромбоцитопенією, підвищенням ШОЕ. При цьому зменшення кількості еритроцитів переважало над зниженням вмісту гемоглобіну, що й дає підстави вважати такий процес гемолітичним.Вже на перших етапах розвитку хвороби виявляється пойкілоцитоз з наявністю ехіноцитів, акантоцитів та стоматоцитів. За третьої стадії хвороби в руслі крові з’являлися уривки еритроцитів (шизоцити) та їх базофільна зернистість.Свідчення про високу потребу організму в кисні за гемолізу підтверджується зростаючою кількістю ретикулоцитів, що посилено вимиваються із кісткового мозку в периферійну кров. Зниження кількості тромбоцитів у крові собак за гострого перебігу бабезіозу відбувається за посиленого їх руйнування та зменшення продукції внаслідок спленомегалії за рахунок секвестрації (депонування) цих клітин крові.За бабезіозу у собак розвивається порушення обміну ферумовмістимих пігментів (гемохроматоз), що підтверджується гіперсидеремією та може свідчити про відкладання феруму у печінці, нирках, м’язах

Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front

We discuss the problem of vacuum structure in light-front field theory in the context of (1+1)-dimensional gauge theories. We begin by reviewing the known light-front solution of the Schwinger model, highlighting the issues that are relevant for reproducing the $\theta$-structure of the vacuum. The most important of these are the need to introduce degrees of freedom initialized on two different null planes, the proper incorporation of gauge field zero modes when periodicity conditions are used to regulate the infrared, and the importance of carefully regulating singular operator products in a gauge-invariant way. We then consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)$/Z_2$, which possesses nontrivial topology. In particular, there are two topological sectors and the physical vacuum state has a structure analogous to a $\theta$ vacuum. We formulate the model using periodicity conditions in $x^\pm$ for infrared regulation, and consider a solution in which the gauge field zero mode is treated as a constrained operator. We obtain the expected $Z_2$ vacuum structure, and verify that the discrete vacuum angle which enters has no effect on the spectrum of the theory. We then calculate the chiral condensate, which is sensitive to the vacuum structure. The result is nonzero, but inversely proportional to the periodicity length, a situation which is familiar from the Schwinger model. The origin of this behavior is discussed.Comment: 29 pages, uses RevTeX. Improved discussion of the physical subspace generally and the vacuum states in particular. Basic conclusions are unchanged, but some specific results are modifie

Shearlets and Optimally Sparse Approximations

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field.Comment: in "Shearlets: Multiscale Analysis for Multivariate Data", Birkh\"auser-Springe

Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

Numerical Simulations of N=(1,1) SYM{1+1} with Large Supersymmetry Breaking

We consider the $N=(1,1)$ SYM theory that is obtained by dimensionally reducing SYM theory in 2+1 dimensions to 1+1 dimensions and discuss soft supersymmetry breaking. We discuss the numerical simulation of this theory using SDLCQ when either the boson or the fermion has a large mass. We compare our result to the pure adjoint fermion theory and pure adjoint boson DLCQ calculations of Klebanov, Demeterfi, and Bhanot and of Kutasov. With a large boson mass we find that it is necessary to add additional operators to the theory to obtain sensible results. When a large fermion mass is added to the theory we find that it is not necessary to add operators to obtain a sensible theory. The theory of the adjoint boson is a theory that has stringy bound states similar to the full SYM theory. We also discuss another theory of adjoint bosons with a spectrum similar to that obtained by Klebanov, Demeterfi, and Bhanot.Comment: 12 pages, 4 figure