7,555 research outputs found

    Some issues about neutrino processes in color superconducting quark matter

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    Several relevant issues in computing neutrino emissivity in Urca processes in color superconducting quark matter are addressed. These include: (1) The constraint on uu quark abundance is given from electric neutrality and the triangle relation among Fermi momenta for participants. (2) The phase space defined by Fermi momentum reduction of quarks is discussed in QCD and NJL model. (3) Fermi effective model of weak interaction is reviewed with special focus on its form in Nambu-Gorkov basis.Comment: Contribution to the proceedings of the Sixth China-Japan Joint Nuclear Physics Symposium, May 16-20, Shanghai China. aipproc format, 8 pages, 5 figure

    Nonlinear Dirac equations on Riemann surfaces

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    We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds. We provide the key analytical steps, i.e., small energy regularity and removable singularity theorems and energy identities for solutions.Comment: to appear in Annals of Global Analysis and Geometr

    Positive Semi-Definiteness and Sum-of-Squares Property of Fourth Order Four Dimensional Hankel Tensors

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    A positive semi-definite (PSD) tensor which is not a sum-of-squares (SOS) tensor is called a PSD non-SOS (PNS) tensor. Is there a fourth order four dimensional PNS Hankel tensor? Until now, this question is still an open problem. Its answer has both theoretical and practical meanings. We assume that the generating vector vv of the Hankel tensor AA is symmetric. Under this assumption, we may fix the fifth element v4v_4 of vv at 11. We show that there are two surfaces M0M_0 and N0N_0 with the elements v2,v6,v1,v3,v5v_2, v_6, v_1, v_3, v_5 of vv as variables, such that M0N0M_0 \ge N_0, AA is SOS if and only if v0M0v_0 \ge M_0, and AA is PSD if and only if v0N0v_0 \ge N_0, where v0v_0 is the first element of vv. If M0=N0M_0 = N_0 for a point P=(v2,v6,v1,v3,v5)P = (v_2, v_6, v_1, v_3, v_5)^\top, then there are no fourth order four dimensional PNS Hankel tensors with symmetric generating vectors for such v2,v6,v1,v3,v5v_2, v_6, v_1, v_3, v_5. Then, we call such a point PP PNS-free. We show that a 4545-degree planar closed convex cone, a segment, a ray and an additional point are PNS-free. Numerical tests check various grid points, and find that they are also PNS-free