2,457 research outputs found
Functional Integral Approach in the Theory of Color Superconductivity
In this series of lectures we present the functional integral method for
studying the superconducting pairing of quarks with the formation of the
diquarks as well as the quark-antiquark pairing in dense QCD. The dynamical
equations for the superconducting order parameters are the nonlinear integral
equations for the composite quantum fields describing the quark-quark or
quark-antiquark systems. These composite fields are the bi-local fields if the
pairing is generated by the gluon exchange while for the instanton induced
pairing interactions they are the local ones. The expressions of the free
energy densities are derived. The binding of three quarks is also discussed.Comment: 21 pages, 2 figures, Lectures at the VIth Vietnam International
School in Theoretical Physics, Vung Tau, 27 December 1999 -- 08 January 200
A convergent relaxation of the Douglas-Rachford algorithm
This paper proposes an algorithm for solving structured optimization
problems, which covers both the backward-backward and the Douglas-Rachford
algorithms as special cases, and analyzes its convergence. The set of fixed
points of the algorithm is characterized in several cases. Convergence criteria
of the algorithm in terms of general fixed point operators are established.
When applying to nonconvex feasibility including the inconsistent case, we
prove local linear convergence results under mild assumptions on regularity of
individual sets and of the collection of sets which need not intersect. In this
special case, we refine known linear convergence criteria for the
Douglas-Rachford algorithm (DR). As a consequence, for feasibility with one of
the sets being affine, we establish criteria for linear and sublinear
convergence of convex combinations of the alternating projection and the DR
methods. These results seem to be new. We also demonstrate the seemingly
improved numerical performance of this algorithm compared to the RAAR algorithm
for both consistent and inconsistent sparse feasibility problems
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