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Generalized space forms
Spaces with radially symmetric curvature at base point p are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to R n or S n under a radially symmetric metric, to RP nExpand
Evolution equation and transport coefficients defined by arrival-time spectra of swarms
Arrival-time spectra of the evolution of swarms in the hydrodynamic regime have been studied theoretically starting from the Boltzmann equation and its eigenvalue problem. In order to express theExpand
Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
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 StokesExpand
Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II
We prove, as our main theorem, the finiteness of topological type of a complete open Riemannian manifold M with a base point p ∈ M whose radial curvature at p is bounded from below by that of aExpand
Magnetic condensation, Abelian dominance, and instability of Savvidy vacuum
Abstract We show that a certain type of color magnetic condensation originating from magnetic monopole configurations is sufficient to provide the mass for off-diagonal gluons in the SU ( 2 )Expand
Kugo-Ojima color confinement criterion and Gribov-Zwanziger horizon condition
Abstract We rewrite the Zwanziger horizon condition in terms of the Kugo–Ojima parameter for color confinement. This enables one to explain which value of the Kugo–Ojima parameter is allowed if theExpand
Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
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 quarkExpand
Vacuum condensate of mass dimension 2 as the origin of mass gap and quark confinement
This is a brief summary of recent works on the possibility of vacuum condensate of mass dimension 2 in Yang-Mills theory as the gluon sector of QCD. In particular, I discuss the physical implicationsExpand
Thirring model as a gauge theory
Abstract We give another reformulation of the Thirring model (with four-fern-don interaction of the current-current type) as a gauge theory and identify it with a gauge-fixed version of theExpand
Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum
We give an argument for deriving analytically the infrared “Abelian” dominance in a gauge invariant way for the Wilson loop average in SU(2) Yang– Mills theory. In other words, we propose a possibleExpand