Finite Transformations and Basis States of <i>SU</i>(<i>n</i>)

Holland, D.F.

doi:10.1063/1.1664779

Cited by 11 publications

(7 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This agrees with the result of Holland [18] but is determined only up to normalization. The normalization is determined by having dV = 1.…”

Section: Iii2 Invariant Volume Elementsupporting

confidence: 91%

Differential geometry on SU(3) with applications to three state systems

Byrd

1998

Journal of Mathematical Physics

View full text Add to dashboard Cite

The left and right invariant vector fields are calculated in an "Euler angle" type parameterization for the group manifold of SU (3), referred to here as Euler coordinates. The corresponding left and right invariant one-forms are then calculated. This enables the calculation of the invariant volume element or Haar measure. These are then used to describe the density matrix of a pure state and geometric phases for three state systems.

show abstract

“…This agrees with the result of Holland [18] but is determined only up to normalization. The normalization is determined by having dV = 1.…”

Section: Iii2 Invariant Volume Elementsupporting

confidence: 91%

Differential geometry on SU(3) with applications to three state systems

Byrd

1998

Journal of Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…One way is to take an arbitrary A E SU (3) This agrees with the result of Holland [7]. This is determined only up to a constant factor since the normalization is determined by setting J d V = 1.…”

Section: Invariant Volume Elementsupporting

confidence: 71%

The geometry of SU(3)

Byrd¹

1997

View full text Add to dashboard Cite

show abstract

“…Similarly, we define the chromofield strength tensor 118) where V P is the plaquette variable for the restricted field (link variable) V , W V and L V represent respectively the Wilson loop operator and the Schwinger line constructed from the restricted field (link variable) V .…”

Section: Chromoelectric Field and Flux Tube Formationmentioning

confidence: 99%

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

et al. 2015

View full text Add to dashboard Cite

The purpose of this paper is to review the recent progress in understanding quark confinement. The emphasis of this review is placed on how to obtain a manifestly gauge-independent picture for quark confinement supporting the dual superconductivity in the Yang-Mills theory, which should be compared with the Abelian projection proposed by 't Hooft. The basic tools are novel reformulations of the YangMills theory based on change of variables extending the decomposition of the SU(N) Yang-Mills field due to Cho, Duan-Ge and Faddeev-Niemi, together with the combined use of extended versions of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the SU(N) Wilson loop operator.Moreover, we give the lattice gauge theoretical versions of the reformulation of the Yang-Mills theory which enables us to perform the numerical simulations on the lattice. In fact, we present some numerical evidences for supporting the dual superconductivity for quark confinement. The numerical simulations include the derivation of the linear potential for static interquark potential, i.e., non-vanishing string tension, in which the "Abelian" dominance and magnetic monopole dominance are established, confirmation of the dual Meissner effect by measuring the chromoelectric flux tube between quark-antiquark pair, the induced magnetic-monopole current, and the type of dual superconductivity, etc. In addition, we give a direct connection between the topological configuration of the Yang-Mills field such as instantons/merons and the magnetic monopole.We show especially that magnetic monopoles in the Yang-Mills theory can be constructed in a manifestly gauge-invariant way starting from the gauge-invariant Wilson loop operator and thereby the contribution from the magnetic monopoles can be extracted from the Wilson loop in a gauge-invariant way through the non-Abelian Stokes theorem for the Wilson loop operator, which is a prerequisite for exhibiting magnetic monopole dominance for quark confinement. The Wilson loop average is calculated according to the new reformulation written in terms of new field variables obtained from the original Yang-Mills field based on change of variables. The Maximally Abelian gauge in the original Yang-Mills theory is also reproduced by taking a specific gauge fixing in the reformulated Yang-Mills theory. This observation justifies the preceding results obtained in the maximal Abelian gauge at least for gaugeinvariant quantities for SU(2) gauge group, which eliminates the criticism of gauge artifact raised for the Abelian projection. The claim has been confirmed based on the numerical simulations.However, for SU(N) (N ≥ 3), such a gauge-invariant reformulation is not unique, although the extension along the line proposed by Cho, Faddeev and Niemi is possible. In fact, we have found that there are a number of possible options of the reformulations, which are discriminated by the maximal stability 1 groupH of G, while there is a unique option ofH = U(1) for G = SU(2). The maximal stability group depends...

show abstract

Finite Transformations and Basis States of SU(n)

Cited by 11 publications

References 5 publications

Differential geometry on SU(3) with applications to three state systems

Differential geometry on SU(3) with applications to three state systems

The geometry of SU(3)

Quark confinement: Dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang–Mills theory

Contact Info

Product

Resources

About