Symmetry and Exact Solutions of the Maxwell and SU(2) Yang–Mills Equations

Zhdanov, Renat; Lahno, V.

doi:10.1002/0471231487.ch3

Cited by 3 publications

(6 citation statements)

References 64 publications

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“…where β = diag(1, 1, −1, −1). From these definitions and from formulas (23) we see that iγ a ∈ su(2, 2) (β = γ 0 ).…”

Section: Constant Solutions Of Yang-mills-proca System Of Equations Imentioning

confidence: 95%

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Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

Marchuk

Shirokov²

2016

JGSP

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ABSTRACT. In this paper we present some new equations which we call Yang-Mills-Proca equations (or generalized Proca equations). This system of equations is a generalization of Proca equation and Yang-Mills equations and it is not gauge invariant. We present a number of constant solutions of this system of equations in the case of arbitrary Lie algebra. In details we consider the case when this Lie algebra is Clifford algebra or Grassmann algebra. We consider solutions of Yang-Mills equations in the form of perturbation theory series near the constant solution.

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“…where β = diag(1, 1, −1, −1). From these definitions and from formulas (23) we see that iγ a ∈ su(2, 2) (β = γ 0 ).…”

Section: Constant Solutions Of Yang-mills-proca System Of Equations Imentioning

confidence: 95%

“…satisfies relations (19) with θ = 1 and the matrices iγ a satisfy conditions (19) with θ = −1. The Hermitian conjugated matrices satisfy conditions (23) (γ a ) † = γ 0 γ a γ 0 , (iγ a ) † = −γ 0 iγ a γ 0 .…”

Section: Anti-commuting Solutions Of Yang-mills-proca Equationsmentioning

confidence: 99%

Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

Marchuk

Shirokov²

2016

JGSP

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“…The explicit expressions for F 2 (35) are (27), (28), (29) respectively for 3 subcases of Case (v) in Lemma 4.…”

Section: Lemmamentioning

confidence: 99%

“…During the last 50 years, many scientists have been searching for particular classes of solutions of the Yang-Mills equations. The well-known classes of solutions of the Yang-Mills equations are described in detail in various reviews [1], [22]. Only certain (nontrivial) classes of particular solutions of these equations are known because of their nonlinearity: monopoles [21], [10], [16], instantons [4], [20], [3], merons [2], etc.…”

Section: Introductionmentioning

confidence: 99%

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On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space ℝⁿ

Shirokov¹

2020

JNMP

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We present classification and explicit form of all constant solutions of the Yang-Mills equations with SU(2) gauge symmetry for an arbitrary constant non-Abelian current in pseudo-Euclidean space R p,q of arbitrary finite dimension n = p + q. We use the method of hyperbolic singular value decomposition and the method of twosheeted covering of orthogonal group by spin group to do this. Nonconstant solutions of the Yang-Mills equations can be considered in the form of series of perturbation theory. The results of this paper are new and can be used to solve some problems in particle physics, in particular, to describe physical vacuum and to fully understand a quantum gauge theory. The results of this paper generalize our previous results for the case of arbitrary Euclidean case R n .

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Gribov Ambiguity

Sainapha

2019

Preprint

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Gribov ambiguity is a problem that arises when we try to single out the physical gauge degree of freedom in non-Abelian gauge theory by imposing the covariant gauge constraint. Unfortunately, the solution of the gauge constraint is not unique, thus the redundant gauge degree of freedom, called Gribov copies, remains unfixed. One of the traditional methods to partially resolve the Gribov problem is to restrict the space of gauge orbits inside the bounded region known as the Gribov region. The meaning of "partially resolve" is that this procedure can solve only the positivity's problem of the Faddeev-Popov operator but the Gribov copies are still there. However, on the bright side, the restriction to the Gribov region leads to the modification of the gluon propagator. Additionally, the new form of the gluon propagator yields the violation of the reflection positivity which is considered as the important axiom of the Euclidean quantum field theory. This shows that the gluon field in the Gribov region is an unphysical particle or technically confined. In this review article, we will start by discussing the traditional Faddeev-Popov method and its consequence on the proof of the unitarity of the perturbative Yang-Mills theory. Next, we will discuss the blind spot of the Faddeev-Popov quantization and study the mathematical and physical origin of the Gribov problem. Then, the method of the Gribov restriction will be elaborated. After that, we demonstrate the modification of the gluon field after restricting inside the bounded Gribov region. Finally, we show that the new form of the gluon leads to the violation of the reflection positivity axiom. i I would like to thank Rujikorn Dhanawittayapol, my supervisor, for allowing me to study what I want to. I want to thank my study group's members, especially, Chawakorn Maneerat, Saksilpa Srisukson and Karankorn Kritsarunont for very useful discussions. I also would like to thank my senior, Sirachak Panpanich, for good suggestions. I'm very grateful to give a special thanks to Kei-Ichi Kondo who give many helpful comments on my thesis. Additionally, I also would like to thank Paolo Bertozzini who gives comments on my axiomatic quantum field theory's part of the thesis. In fact, it is very impressive to thank the organizers of the YKIS2018b to let me participate in the conference which makes me found my research interest. Finally, I want to thank Minase Inori, Yura Hatsuki, Ariabl'eyeS, Yurica/Hanatan, =ME and other bands for very wonderful songs when I feel sick about life.

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Symmetry and Exact Solutions of the Maxwell and SU(2) Yang–Mills Equations

Cited by 3 publications

References 64 publications

Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space ℝⁿ

Gribov Ambiguity

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Symmetry and Exact Solutions of the Maxwell and SU(2) Yang–Mills Equations

Cited by 3 publications

References 64 publications

Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

Constant Solutions of Yang-Mills Equations and Generalized Proca Equations

On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space ℝn

Gribov Ambiguity

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Product

Resources

About

On constant solutions of SU(2) Yang-Mills equations with arbitrary current in Euclidean space ℝⁿ