7,900 research outputs found

    Estimates for parameters and characteristics of the confining SU(3)-gluonic field in neutral kaons and chiral limit for pseudoscalar nonet

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    First part of the paper is devoted to applying the confinement mechanism proposed earlier by the author to estimate the possible parameters of the confining SU(3)-gluonic field in neutral kaons. The estimates obtained are consistent with the widths of the electromagnetic decays K0,Kˉ02γK^0,\bar{K}^0\to2\gamma too. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the mesons under consideration. The second part of the paper takes into account the results obtained previously by the author to estimate the purely gluonic contribution to the masses of all the mesons of pseudoscalar nonet and also to consider a possible relation with a phenomenological string-like picture of confinement. Finally, the problem of masses in particle physics is shortly discussed within the framework of approach to the chiral symmetry breaking in quantum chromodynamics (QCD) proposed recently by the author.Comment: LaTeX, 16 pages, 2 figure

    Hodge correlators II

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    Polylogarithms, regulators and Arakelov motivic complexes

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    We construct an explicit regulator map from the weigh n Bloch Higher Chow group complexto the weight n Deligne complex of a regular complex projective algebraic variety X. We define the Arakelovweight n motivic complex as the cone of this map shifted by one. Its last cohomology group is (a version of) the Arakelov Chow group defined by H. Gillet. and C.Soule. We relate the Grassmannian n-logarithms (defined as in [G5]) to geometry of the symmetric space for GL_n(C). For n=2 we recover Lobachevsky's formula for the volume of an ideal geodesic tetrahedron via the dilogarithm. Using the relationship with symmetric spaces we construct the Borel regulator on K_{2n-1}(C) via the Grassmannian n-logarithms. We study the Chow dilogarithm and prove a reciprocity law which strengthens Suslin's reciprocity law for Milnor's K_3 on curves.Comment: Version 3: It is the final version, as it will appear in JAMS. 71 pages, 12 figure

    Galois symmetries of fundamental groupoids and noncommutative geometry

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    We define motivic iterated integrals on the affine line, and give a simple proof of the formula for the coproduct in the Hopf algebra of they make. We show that it encodes the group law in the automorphism group of certain non-commutative variety. We relate the coproduct with the coproduct in the Hopf algebra of decorated rooted planar trivalent trees - a planar decorated version of the Hopf algebra defined by Connes and Kreimer. As an application we derive explicit formulas for the coproduct in the motivic multiple polylogarithm Hopf algebra. We give a criteria for a motivic iterated integral to be unramified at a prime ideal, and use it to estimate from above the space spanned by the values of iterated integrals. In chapter 7 we discuss some general principles relating Feynman integrals and mixed motives.Comment: 51 pages, The final version to appear in Duke Math.
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