Lagrangian Form of the Self-Dual Equations for SU( N ) Gauge Fields on Four-Dimensional Euclidean Space

1998 ◽  
Vol 29 (3) ◽  
pp. 443-446 ◽  
Author(s):  
Hou Boyu ◽  
Song Xingchang
Keyword(s):  
Euclidean Space ◽  
The Self ◽  
Gauge Fields ◽  
Dimensional Euclidean Space ◽  
Lagrangian Form

scholarly journals An Exact Equation for Wilson Loops in Two-Dimensional Euclidean Space

2003 ◽  
Vol 18 (27) ◽  
pp. 1925-1929
Author(s):  
Mofazzal Azam
Keyword(s):  
Euclidean Space ◽  
Gauge Theories ◽  
Gauge Fields ◽  
Dimensional Euclidean Space ◽  
Exact Equation ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Abelian Gauge

We derive an exact equation for simple self non-intersecting Wilson loops in non-Abelian gauge theories with gauge fields interacting with fermions in two-dimensional Euclidean space.

scholarly journals CLASSIFICATION OF YANG–MILLS FIELDS ADMITTING INTEGRALS OF MOTION FOR THE WONG EQUATIONS

2020 ◽  
pp. 14-24
Author(s):  
M. N. Boldyreva ◽  
A. A. Magazev ◽  
I. V. Shirokov
Keyword(s):  
Euclidean Space ◽  
Three Dimensional ◽  
First Integrals ◽  
Gauge Fields ◽  
Dimensional Euclidean Space ◽  
Integrals Of Motion ◽  
Yang Mills ◽  
Linear Integral

In the paper, we investigate the gauge fields that are characterized by the existence of non-trivial integrals of motion for the Wong equations. For the gauge group 𝑆𝑈(2), the class of fields admitting only the isospin first integrals is described in detail. All gauge non-equivalent Yang–Mills fields admitting a linear integral of motion for the Wong equations are classified in the three-dimensional Euclidean space

scholarly journals Codimension one immersions and the Kervaire invariant one problem

1981 ◽  
Vol 90 (3) ◽  
pp. 483-493 ◽  
Author(s):  
Peter John Eccles
Keyword(s):  
Euclidean Space ◽  
Intersection Point ◽  
The Self ◽  
Dimensional Euclidean Space ◽  
Dimensional Manifold ◽  
Smooth Manifolds ◽  
Codimension One ◽  
Intersection Points

Let i: M↬ℝn+1 be a self-transverse immersion of a compact closed smooth n-dimensional manifold in (n + 1)-dimensional Euclidean space. A point of ℝn+1 is an r-fold intersection point of the immersion if it is the image under i of (at least) r distinct points of the manifold. The self-transversality of i implies that the set of r-fold intersection points is the image of an immersion of a manifold of dimension n+1-r (the empty set if r > n + 1). In particular, the set of (n + l)-fold intersection points is finite of order, say, θ(i). In this paper we are concerned with the set of values of θ(i) for (self-transverse) immersions of all (compact closed smooth) manifolds of given dimension n.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

On Vitali's Theorem for Groups of Motions of Euclidean Space

1999 ◽  
Vol 6 (4) ◽  
pp. 323-334
Author(s):  
A. Kharazishvili
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Finite Dimensional

Abstract We give a characterization of all those groups of isometric transformations of a finite-dimensional Euclidean space, for which an analogue of the classical Vitali theorem [Sul problema della misura dei gruppi di punti di una retta, 1905] holds true. This characterization is formulated in purely geometrical terms.

Some properties of Wigner coefficients and hyperspherical harmonics

1956 ◽  
Vol 52 (3) ◽  
pp. 424-430 ◽  
Author(s):  
A. P. Stone
Keyword(s):  
Angular Momentum ◽  
Euclidean Space ◽  
Rotation Group ◽  
Dimensional Euclidean Space ◽  
Hyperspherical Harmonics ◽  
Shift Operators ◽  
Analytical Relations

ABSTRACTGeneral shift operators for angular momentum are obtained and applied to find closed expressions for some Wigner coefficients occurring in a transformation between two equivalent representations of the four-dimensional rotation group. The transformation gives rise to analytical relations between hyperspherical harmonics in a four-dimensional Euclidean space.

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