Reductions by isometries of the self‐dual Yang–Mills equations in four‐dimensional Euclidean space

1993 ◽  
Vol 34 (7) ◽  
pp. 3245-3268 ◽  
Author(s):  
M. Kovalyov ◽  
M. Légaré ◽  
L. Gagnon
Keyword(s):  
Euclidean Space ◽  
The Self ◽  
Dimensional Euclidean Space ◽  
Yang Mills

The perturbative β-function in the Zumino model

2001 ◽  
Vol 79 (8) ◽  
pp. 1099-1104
Author(s):  
R Clarkson ◽  
D.G.C. McKeon
Keyword(s):  
Euclidean Space ◽  
Dimensional Euclidean Space ◽  
Supersymmetric Model ◽  
Yang Mills ◽  
Β Function ◽  
Zumino Model

We consider the perturbative β-function in a supersymmetric model in four-dimensional Euclidean space formulated by Zumino. It turns out to be equal to the β-function for N = 2 supersymmetric Yang–Mills theory despite differences that exist in the two models. PACS No.: 12.60Jv

scholarly journals INDUCED CONNECTIONS IN FIELD THEORY: THE ODD-DIMENSIONAL YANG–MILLS CASE

1995 ◽  
Vol 10 (07) ◽  
pp. 1005-1017
Author(s):  
DOMENICO GIULINI
Keyword(s):  
Field Theory ◽  
Line Bundle ◽  
Euclidean Space ◽  
Chern Class ◽  
Degrees Of Freedom ◽  
Dimensional Euclidean Space ◽  
Fermion Mass ◽  
Dirac Fermions ◽  
Complex Line ◽  
Yang Mills

We consider SU(N) Yang–Mills theories in (2n + 1)-dimensional Euclidean space–time, where N ≥ n+1, coupled to an even flavor number of Dirac fermions. After integration over the fermionic degrees of freedom, the wave functional for the gauge field inherits a nontrivial U(1) connection which we compute in the limit of infinite fermion mass. Its Chern class turns out to be just half the flavor number, so that the wave functional now becomes a section in a nontrivial complex line bundle. The topological origin of this phenomenon is explained in both the Lagrangian and the Hamiltonian picture.

Operator regularization on the hypersphere

1989 ◽  
Vol 67 (7) ◽  
pp. 669-677 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Euclidean Space ◽  
Sigma Model ◽  
Gauge Theories ◽  
Stereographic Projection ◽  
Mass Parameter ◽  
Field Theories ◽  
Dimensional Euclidean Space ◽  
Two Dimensional ◽  
Yang Mills ◽  
Infrared Cutoff

Operator regularization has proved to be a viable way of computing radiative corrections that avoids both the insertion of a regulating parameter into the initial Lagrangian and the occurrence of explicit infinities at any stage of the calculation. We show how this regulating technique can be used in conjunction with field theories defined on an n + 1-dimensional hypersphere, which is the stereographic projection of n-dimensional Euclidean space. The radius of the hypersphere acts as an infrared cutoff, thus eliminating the need to insert a mass parameter to serve as an infrared regulator. This has the advantage of leaving conformai symmetry present in massless theories, intact. We illustrate our approach by considering [Formula: see text], massless Yang–Mills gauge theories and the two-dimensional nonlinear bosonic sigma model with torsion. In the last model, the lowest mode is used as an infrared cutoff.

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.

QUATERNIONIC (ALIAS Sp(2)) COHERENT STATE AND HILBERT CONNECTION

1990 ◽  
Vol 05 (22) ◽  
pp. 1765-1772 ◽  
Author(s):  
HIROSHI KURATSUJI ◽  
KENICHI TAKADA
Keyword(s):  
Euclidean Space ◽  
Coherent State ◽  
Projective Space ◽  
Gauge Field ◽  
Path Integral ◽  
Topological Invariant ◽  
Dimensional Euclidean Space ◽  
Quaternionic Projective Space ◽  
Yang Mills ◽  
State Path

The Hilbert (or quantum) connection defined via the quaternionic (or Sp(2)) coherent state is studied by using coherent state path integral. This gives a non-integrable phase associated with the Yang-Mills gauge field induced on the compactified 4-dimensional Euclidean space S4(≃ P1(H) quaternionic projective space). The topological invariant is also discussed.

scholarly journals NON-ABELIAN BERRY PHASE, YANG–MILLS INSTANTON AND USp(2k) MATRIX MODEL

1999 ◽  
Vol 14 (13) ◽  
pp. 869-877 ◽  
Author(s):  
B. CHEN ◽  
H. ITOYAMA ◽  
H. KIHARA
Keyword(s):  
Quantum Mechanics ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Matrix Model ◽  
Berry Phase ◽  
Space Time ◽  
Dimensional Euclidean Space ◽  
Yang Mills ◽  
Time Points

The non-Abelian Berry phase is computed in the T dualized quantum mechanics obtained from the USp (2k) matrix model. Integrating the fermions, we find that each of the space–time points [Formula: see text] is equipped with a pair of su(2) Lie algebra valued pointlike singularities located at a distance m(f) from the orientifold surface. On a four-dimensional paraboloid embedded in the five-dimensional Euclidean space, these singularities are recognized as the BPST instantons.

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