Pure bosonic world-line path integral representation for fermionic determinants, non-Abelian Stokes theorem, and quasiclassical approximation in QCD

Lunev, F. A.

doi:10.1016/s0550-3213(97)00154-5

Cited by 12 publications

(19 citation statements)

References 71 publications

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“…Rather, we claim that even in the SU(N) Yang-Mills theory a single magnetic monopole is sufficient to achieve confinement, when quarks belong to the fundamental representation of the color gauge group. In fact, this scenario was originally proposed in [59,60,61] based on a consideration from a non-Abelian Stokes theorem for the Wilson loop operator [55,56,57,58], which is more elaborated in [62,63,64,65] (See [66,67,68,69,70,71,72] for other versions of non-Abelian Stokes theorem). In order to consider confinement of quarks in the specified representation based on the Wilson loop operator, we adopt the color field n(x) taking the value in the Lie algebra of G/H, 14) whereH is a subgroup of G called the maximal stability subgroup which is determined once the highest-weight state of a given representation is chosen.…”

Section: 3)mentioning

confidence: 99%

“…In contrast to the ordinary Stokes theorem, there exist many versions for the non-Abelian Stokes theorem (NAST) [55,56,67,68,69,70,71,72]. In this section, we treat a version of the NAST derived by Diakonov and Petrov [55,56].…”

Section: Wilson Loop Operator Via a Non-abelian Stokes Theoremmentioning

confidence: 99%

“…Therefore, there exists some deviation on a lattice coming from non-zero lattice spacing ǫ > 0. 71 • The strong "Abelian" dominance does NOT immediately imply the dominance of the Wilson loop average for arbitrary closed loop C:…”

Section: Gauge-independent "Abelian" Dominance For the Wilson Loop Opmentioning

confidence: 99%

“…is rewritten in terms of the surface integral over the surface Σ bounded by the closed loop C, the the Wilson loop operator is rewritten in terms of the 71 In [64], the result obtained for SU (2) in the continuum formulation was extended to the SU (N ) on the lattice and in the continuum. A constructive proof was given by deriving the lattice regularized version of the non-Abelian Stokes theorem and the lattice versions of the gauge field decomposition which have been constructed and developed for SU (2) in [27,28] and for SU (N ) in [30,31] according to the continuum versions given in [18] and [24], respectively.…”

Section: Gauge-independent "Abelian" Dominance For the Wilson Loop Opmentioning

confidence: 99%

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

et al. 2015

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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...

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Section: 3)mentioning

confidence: 99%

Section: Wilson Loop Operator Via a Non-abelian Stokes Theoremmentioning

confidence: 99%

Section: Gauge-independent "Abelian" Dominance For the Wilson Loop Opmentioning

confidence: 99%

Section: Gauge-independent "Abelian" Dominance For the Wilson Loop Opmentioning

confidence: 99%

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

et al. 2015

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“…[5] and that the same form for the NAST has been derived in an independent way specifically for the fundamental representation of the SU (N ) gauge group in [18]. However, the formula given there is not appropriate for our purpose stated above.…”

Section: Introductionmentioning

confidence: 99%

Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement

Matsudo

Kondo

2015

Phys. Rev. D

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We give a gauge-independent definition of magnetic monopoles in the SU (N ) Yang-Mills theory through the Wilson loop operator. For this purpose, we give an explicit proof of the DiakonovPetrov version of the non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation of the SU (N ) gauge group to derive a new form for the non-Abelian Stokes theorem. The new form is used to extract the magnetic-monopole contribution to the Wilson loop operator in a gauge-invariant way, which enables us to discuss confinement of quarks in any representation from the viewpoint of the dual superconductor vacuum.

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Loop and Path Spaces and�Four-Dimensional BF Theories:�Connections, Holonomies and Observables

Cattaneo¹,

Cotta-Ramusino²,

Rinaldi³

1999

Communications in Mathematical Physics

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We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M . In particular we consider connections defined in terms of pairs (A, B), where A is a connection for a fixed principal bundle P (M, G) and B is a 2-form on M . The relevant curvatures, parallel transports and holonomies are computed and their expressions in local coordinates are exhibited. When the 2-form B is given by the curvature of A, then the so-called non-abelian Stokes formula follows.For a generic 2-form B, we distinguish the cases when the parallel transport depends on the whole path of paths and when it depends only on the spanned surface. In particular we discuss generalizations of the non-abelian Stokes formula. We study also the invariance properties of the (trace of the) holonomy under suitable transformation groups acting on the pairs (A, B).In this way we are able to define observables for both topological and non-topological quantum field theories of the BF type. In the non topological case, the surface terms may be relevant for the understanding of the quark-confinement problem. In the topological case the (perturbative) fourdimensional quantum BF -theory is expected to yield invariants of imbedded (or immersed) surfaces in a 4-manifold M .

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Pure bosonic world-line path integral representation for fermionic determinants, non-Abelian Stokes theorem, and quasiclassical approximation in QCD

Cited by 12 publications

References 71 publications

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

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

Non-Abelian Stokes theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement

Loop and Path Spaces and�Four-Dimensional BF Theories:�Connections, Holonomies and Observables

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