The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Kei-ichi Kondo - One of the best experts on this subject based on the ideXlab platform.
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Non-Abelian Stokes Theorem for the Wilson loop operator in an arbitrary representation and its implication to quark confinement
Physical Review D, 2015Co-Authors: Ryutaro Matsudo, Kei-ichi KondoAbstract: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 Diakonov-Petrov 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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quark confinement dual superconductor picture based on a non abelian Stokes Theorem and reformulations of yang mills theory
Physics Reports, 2015Co-Authors: Kei-ichi Kondo, Seikou Kato, Akihiro Shibata, Toru ShinoharaAbstract:Abstract 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 Yang–Mills theory based on change of variables extending the decomposition of the S U ( 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 S U ( 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 gauge-invariant quantities for S U ( 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 S U ( 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 group H of G , while there is a unique option of H = U ( 1 ) for G = S U ( 2 ) . The maximal stability group depends on the representation of the gauge group, to that the quark source belongs. For the fundamental quark for S U ( 3 ) , the maximal stability group is U ( 2 ) , which is different from the maximal torus group U ( 1 ) × U ( 1 ) suggested from the Abelian projection. Therefore, the chromomagnetic monopole inherent in the Wilson loop operator responsible for confinement of quarks in the fundamental representation for S U ( 3 ) is the non-Abelian magnetic monopole, which is distinct from the Abelian magnetic monopole for the S U ( 2 ) case. Therefore, we claim that the mechanism for quark confinement for S U ( N ) ( N ≥ 3 ) is the non-Abelian dual superconductivity caused by condensation of non-Abelian magnetic monopoles. We give some theoretical considerations and numerical results supporting this picture. Finally, we discuss some issues to be investigated in future studies.
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Quark confinement: dual superconductor picture based on a non-Abelian Stokes Theorem and reformulations of Yang-Mills theory
Physics Reports, 2015Co-Authors: Kei-ichi Kondo, Seikou Kato, Akihiro Shibata, Toru ShinoharaAbstract: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 Yang-Mills 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.
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Wilson loop and magnetic monopole through a non-Abelian Stokes Theorem
Physical Review D, 2008Co-Authors: Kei-ichi KondoAbstract:I show that the Wilson loop operator for the SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes Theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang-Mills theory even in the absence of the Higgs scalar field, in sharp contrast to the 't Hooft-Polyakov magnetic monopole in the Georgi-Glashow gauge-Higgs model. The resulting representation indicates that the Wilson loop operator in fundamental representations can be a probe for a single magnetic monopole irrespective of N in SU(N) Yang-Mills theory, against the conventional wisdom. Moreover, I show that the quantization condition for the magnetic charge follows from the fact that the non-Abelian Stokes Theorem does not depend on the surface chosen for writing the surface integral. The obtained geometrical and topological representations of the Wilson loop operator have important implications to understanding quark confinement according to the dual superconductor picture.
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Non-Abelian Stokes Theorem and Quark Confinement in SU(N) Yang-Mills Gauge Theory
Progress of Theoretical Physics, 2000Co-Authors: Kei-ichi Kondo, Yutaro TairaAbstract:We derive a new version of SU(3) non-Abelian Stokes Theorem by making use of the coherent state representation on the coset space SU(3)/(U(1) × U(1)) = F2, the flag space. Then we outline a derivation of the area law of the Wilson loop in SU(3) Yang-Mills theory in the maximal Abelian gauge (The detailed exposition will be given in a forthcoming article). This derivation is performed by combining the non-Abelian Stokes Theorem with the reformulation of the Yang-Mills theory as a perturbative deformation of a topological field theory recently proposed by one of the authors. Within this framework, we show that the fundamental quark is confined even if G = SU(3) is broken by partial gauge fixing into H = U(2) just as G is broken to H = U(1) × U(1). An origin of the area law is related to the geometric phase of the Wilczek-Zee holonomy for U(2). Abelian dominance is an immediate byproduct of these results and magnetic monopole plays the dominant role in this derivation.
Toru Shinohara - One of the best experts on this subject based on the ideXlab platform.
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quark confinement dual superconductor picture based on a non abelian Stokes Theorem and reformulations of yang mills theory
Physics Reports, 2015Co-Authors: Kei-ichi Kondo, Seikou Kato, Akihiro Shibata, Toru ShinoharaAbstract:Abstract 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 Yang–Mills theory based on change of variables extending the decomposition of the S U ( 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 S U ( 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 gauge-invariant quantities for S U ( 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 S U ( 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 group H of G , while there is a unique option of H = U ( 1 ) for G = S U ( 2 ) . The maximal stability group depends on the representation of the gauge group, to that the quark source belongs. For the fundamental quark for S U ( 3 ) , the maximal stability group is U ( 2 ) , which is different from the maximal torus group U ( 1 ) × U ( 1 ) suggested from the Abelian projection. Therefore, the chromomagnetic monopole inherent in the Wilson loop operator responsible for confinement of quarks in the fundamental representation for S U ( 3 ) is the non-Abelian magnetic monopole, which is distinct from the Abelian magnetic monopole for the S U ( 2 ) case. Therefore, we claim that the mechanism for quark confinement for S U ( N ) ( N ≥ 3 ) is the non-Abelian dual superconductivity caused by condensation of non-Abelian magnetic monopoles. We give some theoretical considerations and numerical results supporting this picture. Finally, we discuss some issues to be investigated in future studies.
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Quark confinement: dual superconductor picture based on a non-Abelian Stokes Theorem and reformulations of Yang-Mills theory
Physics Reports, 2015Co-Authors: Kei-ichi Kondo, Seikou Kato, Akihiro Shibata, Toru ShinoharaAbstract: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 Yang-Mills 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.
F.a. Lunev - One of the best experts on this subject based on the ideXlab platform.
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Pure bosonic world-line path integral representation for fermionic determinants, non-Abelian Stokes Theorem, and quasiclassical approximation in QCD
Nuclear Physics B, 1997Co-Authors: F.a. LunevAbstract:Simple bosonic path integral representation for path ordered exponent is derived. This representation is used, at first, to obtain new variant of non-Abelian Stokes Theorem. Then new pure bosonic worldline path integral representations for fermionic determinant and Green functions are presented. Finally, applying stationary phase method, we get quasiclassical equations of motion in QCD.Comment: LaTeX, 49 page
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pure bosonic world line path integral representation for fermionic determinants non abelian Stokes Theorem and quasiclassical approximation in qcd
Nuclear Physics, 1997Co-Authors: F.a. LunevAbstract:Abstract A simple bosonic path integral representation for the path ordered exponent is derived. This representation is used, first, to obtain a new variant of the non-Abelian Stokes Theorem. Then new pure bosonic world-line path integral representations for the fermionic determinant and Green functions are presented. Finally, applying the stationary phase method, we get the quasiclassical equations of motion in QCD.
Freydoon Mansouri - One of the best experts on this subject based on the ideXlab platform.
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Product Integral Representations of Wilson Lines and Wilson Loops and Non-Abelian Stokes Theorem
Turkish journal of physics, 2000Co-Authors: Robert L Karp, Freydoon Mansouri, Jung S RnoAbstract:We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of Wilson lines and Wilson loops as approximating them with partial sums, their convergence, and their behavior under gauge transformations. We also obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes Theorem.
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Supersymmetric Wilson Lines and Loops, and Super Non-Abelian Stokes Theorem
Physics Letters B, 2000Co-Authors: Robert L Karp, Freydoon MansouriAbstract:We generalize the standard product integral formalism to incorporate Grassmann valued matrices and show that the resulting supersymmetric product integrals provide a natural framework for describing supersymmetric Wilson Lines and Wilson Loops. We use this formalism to establish the supersymmetric version of the non-Abelian Stokes Theorem.
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product integral formalism and non abelian Stokes Theorem
arXiv: High Energy Physics - Theory, 1999Co-Authors: Robert L Karp, Freydoon Mansouri, Jung S RnoAbstract:We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' Theorem.
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Product Integral Representations of Wilson Lines and Wilson Loops, and Non-Abelian Stokes Theorem
arXiv: High Energy Physics - Theory, 1999Co-Authors: Robert L Karp, Freydoon Mansouri, Jung S RnoAbstract:We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as approximating them with partial sums, their convergence, and their behavior under gauge transformations. We also obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes Theorem.
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Supersymmetric Wilson Loops and Super Non-Abelian Stokes Theorem
Confluence of Cosmology Massive Neutrinos Elementary Particles and Gravitation, 1Co-Authors: Robert L Karp, Freydoon MansouriAbstract:We generalize the standard product integral formalism to supersymmetric product integrals. Using these, we provide an unambiguous mathematical representation of supersymmetric Wilson line and Wilson loop operators and study their properties. We also prove the supersymmetric version of non-abelian Stokes Theorem.
Akihiro Shibata - One of the best experts on this subject based on the ideXlab platform.
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quark confinement dual superconductor picture based on a non abelian Stokes Theorem and reformulations of yang mills theory
Physics Reports, 2015Co-Authors: Kei-ichi Kondo, Seikou Kato, Akihiro Shibata, Toru ShinoharaAbstract:Abstract 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 Yang–Mills theory based on change of variables extending the decomposition of the S U ( 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 S U ( 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 gauge-invariant quantities for S U ( 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 S U ( 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 group H of G , while there is a unique option of H = U ( 1 ) for G = S U ( 2 ) . The maximal stability group depends on the representation of the gauge group, to that the quark source belongs. For the fundamental quark for S U ( 3 ) , the maximal stability group is U ( 2 ) , which is different from the maximal torus group U ( 1 ) × U ( 1 ) suggested from the Abelian projection. Therefore, the chromomagnetic monopole inherent in the Wilson loop operator responsible for confinement of quarks in the fundamental representation for S U ( 3 ) is the non-Abelian magnetic monopole, which is distinct from the Abelian magnetic monopole for the S U ( 2 ) case. Therefore, we claim that the mechanism for quark confinement for S U ( N ) ( N ≥ 3 ) is the non-Abelian dual superconductivity caused by condensation of non-Abelian magnetic monopoles. We give some theoretical considerations and numerical results supporting this picture. Finally, we discuss some issues to be investigated in future studies.
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Quark confinement: dual superconductor picture based on a non-Abelian Stokes Theorem and reformulations of Yang-Mills theory
Physics Reports, 2015Co-Authors: Kei-ichi Kondo, Seikou Kato, Akihiro Shibata, Toru ShinoharaAbstract: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 Yang-Mills 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.