Pseudoparticle Solutions of the Yang-Mills Equations

We review investigations on defects in systems described by real scalar fields in (D, 1) space-time dimensions. We first work in one spatial dimension, with models described by one and two real scalar fields, and in higher dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We also show how to find first-order differential equations that solve the equations of motion, and how to solve models in D dimensions via soluble problems in D = 1. We illustrate the procedure examining specific models and showing how they may be used in applications in different contexts in condensed matter physics, and in other areas.

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“…The model maps an old solution, shown in Ref. [50]. It reproduces topological solitons in magnetic systems, as one can see in Ref.…”

Section: Two or More Spatial Dimensionssupporting

confidence: 62%

Global Defects in Field Theory With Applications to Condensed Matter

Bazeia

Menezes

2005

Mod. Phys. Lett. B

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“…After the discovery of instantons [1] it became clear that quantum mechanics of the vacuum state in non-abelian gauge theories is non-trivial. Thus, in QCD it was shown that a non-contractible path in the space of fields exists, i.e., one of the directions in the (infinitely dimensional) functional space is a closed circle.…”

Section: Introductionmentioning

confidence: 99%

“…Indeed, in such theories the gaugino condensate λλ is non-vanishing and, moreover, exactly calculable [5]. The calculation is based on a theorem establishing the holomorphic dependence of λλ on certain parameters in the SUSYM Lagrangian [6] (for a brief review see the Reprint Volume cited in [1]). While the direct calculation [5] proves that λλ = 0 the standard pattern [2,3] with one circle of unit length in the K direction (K is the Chern-Simons charge; see Fig.…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanics of the vacuum state in two-dimensional QCD with adjoint fermions

1995

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A study of two-dimensional QCD on a spatial circle with Majorana fermions in the adjoint representation of the gauge groups SU(2) and SU(3) has been performed. The main emphasis is put on the symmetry properties related to the homotopically non-trivial gauge transformations and the discrete axial symmetry of this model. Within a gauge fixed canonical framework, the delicate interplay of topology on the one hand and Jacobians and boundary conditions arising in the course of resolving Gauss's law on the other hand is exhibited. As a result, a consistent description of the residual Z N gauge symmetry (for SU(N)) and the "axial anomaly" emerges. For illustrative purposes, the vacuum of the model is determined analytically in the limit of a small circle. There, the Born-Oppenheimer approximation is justified and reduces the vacuum problem to simple quantum mechanics. The issue of fermion condensates is addressed and residual discrepancies with other approaches are pointed out.

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“…The partial solution of this class was first written as a rational polynomial in z by Belavin and Polyakov [9] and can be thought as a superposition of vortices. There are other solutions whose applications to the magnetism of small cylindrical particles are given elsewhere [10].…”

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confidence: 99%

Simple analytical description for the cross-tie domain wall structure

Metlov

2001

Applied Physics Letters

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A closed form analytical expression for the magnetization vector distribution within the cross-tie domain wall in an isotropic ferromagnetic thin film is given. The expression minimizes the exchange energy functional exactly, and the magnetostatic energy by means of an adjustable parameter (wall width). The equilibrium value of the wall width and the film thickness corresponding to the transition between the Néel and the cross-tie walls are calculated. The results are compared with the recent experiments and are in good qualitative agreement.The structure of magnetic domain walls (transition regions separating magnetic domains) was in a focus of extensive research in 1930s -60s and during the time a lot of useful results on the static structures of various wall types as well as their dynamic properties were obtained. Many of the results on the theory of the domain walls can be found in books [1,2]. In particular, there are analytical expressions for the distribution of the magnetization vector inside of the one-dimensional Bloch and Néel domain walls, which are the starting point for calculating their static and dynamic properties.The cross-tie domain wall was also observed in a number of experiments a that time (see Ref.3 and references therein) and also with modern high resolution techniques [4,5,6], and are usual in thin and ultra-thin magnetic films important for modern applications [7]. However, there is no [4] (also see p. 163 in Ref.2) closed form analytical expression for the cross-tie wall structure. This is, probably, due to the fact that magnetization distribution even in straight cross-tie domain wall is two-dimensional (unlike one-dimensional ones of Bloch and Néel walls). It means, the structure of such a wall is defined by a system of non-linear integral (due to the long-range dipolar interactions) partial differential equations, and there is no way to reduce this system to a single equation (as it was done for the Néel wall [8]).Consider a thin film having the thickness h made of soft (isotropic) magnetic material, in the Cartesian coordinate system X, Y , Z chosen in such a way that 0Z axis is perpendicular to the film plane. The parameters of the material entering the calculation are the exchange constant C, and the saturation magnetization constant M S . If the film is thin enough, so that h is of the order of a few exchange lengths L E = C/M 2 S , the dependence of the magnetization distribution on Z can be neglected and the task becomes essentially two-dimensional. If we also neglect the dipolar interaction for a while, the magnetization distribution M ( r) = M S m( r), | m| = 1, r = {X, Y } is defined by the minimum of the exchange energy functional:where the integration runs over all X − Y plane. The last expression is given using the parametrization of the magnetization vector field by a complex function w(z, z) of a complex variable z = X+ıY , ı = √ −1, line over a variable means complex conjugation, so that m x +ım y = 2w/(1+ww) and m z = (1−ww)/(1+ww), ∂/∂z = (∂/∂X −ı∂/∂X)/2, ∂/∂z = (∂...

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Pseudoparticle Solutions of the Yang-Mills Equations

Cited by 281 publications

References 0 publications

Global Defects in Field Theory With Applications to Condensed Matter

Global Defects in Field Theory With Applications to Condensed Matter

Quantum mechanics of the vacuum state in two-dimensional QCD with adjoint fermions

Simple analytical description for the cross-tie domain wall structure

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