10,169 research outputs found
Block diagonal dominance for systems of nonlinear equations with application to load flow calculations in power systems
AbstractThe concept of a pointwise strict (or Ω) diagonally dominant nonlinear function, first introduced by Moré, is generalized to the blockwise case. A sufficient condition is obtained for the convergence of underrelaxed block Jacobi and block Gauss– Seidel iterations for a nonlinear system of equations in terms of the strict (or Ω) diagonal dominance of an associated matrix. A new formulation for the determination of the steady-state load flow in lossless electric power systems is described and it is shown that this formulation leads to the solution of a system of quadratic equations in the unknown (complex-valued) voltages. Under suitable assumptions on the power system the sufficient condition is satisfied. Numerical examples, consisting of an illustrative three bus system and a realistic thirty bus system, are presented. Results of our block Gauss–Seidel iteration are compared with those of Newton–Raphson iteration
Off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
We investigate a dynamical mass generation mechanism for the off-diagonal
gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal
Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in
that gauge. It originates from the condensation of a mixed gluon-ghost operator
of mass dimension two, which lowers the vacuum energy. We construct an
effective potential for this operator by a combined use of the local composite
operators technique with algebraic renormalization and we discuss the gauge
parameter independence of the results. We also show that it is possible to
connect the vacuum energy, due to the mass dimension two condensate discussed
here, with the non-trivial vacuum energy originating from the condensate ,
which has attracted much attention in the Landau gauge.Comment: 15 pages. Revtex. 1 .eps figure. Talk given by D.Dudal at XXV
Encontro Nacional de Fisica de Particulas e Campos, Caxambu, Minas Gerais,
Brasil, 24-28 Aug 2004. To appear in Brazilian Journal of Physic
Ordering of Energy Levels for Extended SU(N) Hubbard Chain
The Lieb-Mattis theorem on the antiferromagnetic ordering of energy levels is
generalized to SU(N) extended Hubbard model with Heisenberg exchange and
pair-hopping terms. It is proved that the minimum energy levels among the
states from equivalent representations are nondegenerate and ordered according
to the dominance order of corresponding Young diagrams. In particular, the
ground states form a unique antisymmetric multiplet. The relation with the
similar ordering among the spatial wavefunctions with different symmetry
classes of ordinary quantum mechanics is discussed also
Yang-Mills Theory as a Deformation of Topological Field Theory, Dimensional Reduction and Quark Confinement
We propose a reformulation of Yang-Mills theory as a perturbative deformation
of a novel topological (quantum) field theory. We prove that this reformulation
of the four-dimensional QCD leads to quark confinement in the sense of area law
of the Wilson loop. First, Yang-Mills theory with a non-Abelian gauge group G
is reformulated as a deformation of a novel topological field theory. Next, a
special class of topological field theories is defined by both BRST and
anti-BRST exact action corresponding to the maximal Abelian gauge leaving the
maximal torus group H of G invariant. Then we find the topological field theory
() has a hidden supersymmetry for a choice of maximal Abelian gauge. As a
result, the D-dimensional topological field theory is equivalent to the
(D-2)-dimensional coset G/H non-linear sigma model in the sense of Parisi and
Sourlas dimensional reduction. After maximal Abelian gauge fixing, the
topological property of magnetic monopole and anti-monopole of four-dimensional
Yang-Mills theory is translated into that of instanton and anti-instanton in
two-dimensional equivalent model. It is shown that the linear static potential
in four-dimensions follows from the instanton--anti-instanton gas in the
equivalent two-dimensional non-linear sigma model obtained from the
four-dimensional topological field theory by dimensional reduction, while the
remaining Coulomb potential comes from the perturbative part in
four-dimensional Yang-Mills theory. The dimensional reduction opens a path for
applying various exact methods developed in two-dimensional quantum field
theory to study the non-perturbative problem in low-energy physics of
four-dimensional quantum field theories.Comment: 58 pages, Latex, no figures, version accepted for publication in
Phys. Rev. D (additions of Discussion, references and minor changes
An analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
We investigate a dynamical mass generation mechanism for the off-diagonal
gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal
Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in
that gauge. It originates from the condensation of a mixed gluon-ghost operator
of mass dimension two, which lowers the vacuum energy. We construct an
effective potential for this operator by a combined use of the local composite
operators technique with the algebraic renormalization and we discuss the gauge
parameter independence of the results. We also show that it is possible to
connect the vacuum energy, due to the mass dimension two condensate discussed
here, with the non-trivial vacuum energy originating from the condensate ,
which has attracted much attention in the Landau gauge.Comment: 24 pages, 2 .eps figures. v2: version accepted for publication in
Phys.Rev.
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