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 THE BOUSSINESQ HIERARCHY AND REALIZATION OF W3-SYMMETRY

1993 ◽  
Vol 08 (05) ◽  
pp. 895-907
Author(s):  
S. GHOSH ◽  
S. ROY
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Lie Algebra ◽  
Ward Identity ◽  
Gauge Fields ◽  
Scalar Field Theory ◽  
Gauge Fixing ◽  
Free Scalar

The Boussinesq hierarchy equation can be regarded as W3-gravity Ward identity from Polyakov-type gauge fixing on SL (3, R) Lie algebra valued gauge fields through proper identification of the fields. We clarify its relation with the W3-gravity obtained by Hull through gauging the chiral W3-symmetry of a free scalar field theory.

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 ON GENERALIZED SELF-DUALITY EQUATIONS TOWARDS SUPERSYMMETRIC QUANTUM FIELD THEORIES OF FORMS

1998 ◽  
Vol 13 (14) ◽  
pp. 1115-1132 ◽  
Author(s):  
LAURENT BAULIEU ◽  
CÉLINE LAROCHE
Keyword(s):  
The Self ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Time Dimension ◽  
Yang Mills ◽  
Self Duality ◽  
Topological Quantum ◽  
Gauge Functions

We classify possible "self-duality" equations for p-form gauge fields in space–time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang–Mills fields (p=1) in 4<D≤8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T-invariant under a subgroup H of SO D. Second, the representation for the SO D curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the "self-duality" equations can be candidates of gauge functions for SO D-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for D≥10 for various p-form gauge fields.

Self-Dual Solutions for SU(2) and SU(3) Gauge Fields on Euclidean Space

2004 ◽  
Vol 43 (1) ◽  
pp. 151-159 ◽  
Author(s):  
A. H. Khater ◽  
D. K. Callebaut ◽  
R. M. Shehata ◽  
S. M. Sayed
Keyword(s):  
Euclidean Space ◽  
Dual Solutions ◽  
Gauge Fields

scholarly journals Chirality, a new key for the definition of the connection and curvature of a Lie-Kac superalgebra

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jean Thierry-Mieg
Keyword(s):  
Scalar Field ◽  
Lie Algebra ◽  
Bianchi Identity ◽  
Parallel Transport ◽  
Lie Superalgebra ◽  
Natural Generalization ◽  
Yang Mills ◽  
Complex Functions ◽  
Definition Of ◽  
Mills Field

Abstract A natural generalization of a Lie algebra connection, or Yang-Mills field, to the case of a Lie-Kac superalgebra, for example SU(m/n), just in terms of ordinary complex functions and differentials, is proposed. Using the chirality χ which defines the supertrace of the superalgebra: STr(…) = Tr(χ…), we construct a covariant differential: D = χ(d + A) + Φ, where A is the standard even Lie-subalgebra connection 1-form and Φ a scalar field valued in the odd module. Despite the fact that Φ is a scalar, Φ anticommutes with (χA) because χ anticommutes with the odd generators hidden in Φ. Hence the curvature F = DD is a superalgebra-valued linear map which respects the Bianchi identity and correctly defines a chiral parallel transport compatible with a generic Lie superalgebra structure.

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.

scholarly journals GENERALIZED GAUGE THEORIES AND THE WEINBERG–SALAM MODEL WITH DIRAC–KÄHLER FERMIONS

2001 ◽  
Vol 16 (23) ◽  
pp. 3867-3895 ◽  
Author(s):  
NOBORU KAWAMOTO ◽  
HIROSHI UMETSU ◽  
TAKUYA TSUKIOKA
Keyword(s):  
Gauge Theory ◽  
Lie Algebra ◽  
Noncommutative Geometry ◽  
Gauge Theories ◽  
Differential Forms ◽  
Gauge Fields ◽  
Present Formulation ◽  
Yang Mills ◽  
Graded Lie Algebra ◽  
Chern Simons

We extend the previously proposed generalized gauge theory formulation of the Chern–Simons type and topological Yang–Mills type actions into Yang–Mills type actions. We formulate gauge fields and Dirac–Kähler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one-form gauge fields accommodated with the graded Lie algebra of SU (2|1) supergroup leads the Weinberg–Salam model. Thus the Weinberg–Salam model formulated by noncommutative geometry is a particular example of the present formulation.

SOLUTIONS TO YANG–MILLS EQUATIONS: QUASI-INSTANTONS, QUASI-MONOPOLES AND QUASI-VORTICES

1992 ◽  
Vol 07 (02) ◽  
pp. 269-285 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Lie Groups ◽  
Sigma Model ◽  
String Model ◽  
Gauge Fields ◽  
Relativistic String ◽  
Yang Mills ◽  
Self Duality ◽  
Model Equations ◽  
The One ◽  
Real Forms

Yang–Mills equations for semisimple gauge Lie groups G in d = 4 spaces with signatures (+ + + +) and (+ + − −) are considered. Generalizations of the one-monopole and one-instanton solutions to these equations for the group [Formula: see text] and for its real forms are obtained. For gauge fields of the vortex type, the Ansätze permitting the reduction of d = 4 self-duality equations to the d = 2 Liouville, sinh–Gordon and sine–Gordon, G/H sigma-model equations and to the equations of the relativistic string model are presented.

scholarly journals Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time

2016 ◽  
Vol 31 (33) ◽  
pp. 1650188 ◽  
Author(s):  
David Benisty ◽  
E. I. Guendelman
Keyword(s):  
Scalar Field ◽  
Maxwell Equations ◽  
Killing Vector ◽  
Gravitational Theory ◽  
Gauge Fields ◽  
Conformal Killing ◽  
Spatial Curvature ◽  
Yang Mills ◽  
Dynamical Time ◽  
The Universe

Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang–Mills equations, for more general spacetimes.

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