Monopoles and Knots in Skyrme Theory

We show that the Skyrme theory actually is a theory of monopoles which allows a new type of solitons, the topological knots made of monopole-anti-monopole pair,which is different from the well-known skyrmions. Furthermore, we derive a generalized Skyrme action from the Yang-Mills action of QCD, which we propose to be an effective action of QCD in the infra-red limit. We discuss the physical implications of our results.Comment: 4 pages. Phys. Rev. Lett. in pres

Refinements of Some Reverses of Schwarz's Inequality in 2-Inner Product Spaces and Applications for Integrals

Refinements of some recent reverse inequalities for the celebrated Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided

Some Boas-Bellman Type Inequalities in 2-Inner Product Spaces

Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided

Color Reflection Invariance and Monopole Condensation in QCD

We review the quantum instability of the Savvidy-Nielsen-Olesen (SNO) vacuum of the one-loop effective action of SU(2) QCD, and point out a critical defect in the calculation of the functional determinant of the gluon loop in the SNO effective action. We prove that the gauge invariance, in particular the color reflection invariance, exclude the unstable tachyonic modes from the gluon loop integral. This guarantees the stability of the magnetic condensation in QCD.Comment: 28 pages, 3 figures, JHEP styl