We discuss the physical impacts of the "Cho decomposition" (or the "Cho-Faddeev-Niemi-Shabanov decomposition") of the non-Abelian gauge potential on QCD. We show how the decomposition makes a subtle but important modification on the non-Abelian dynamics, and present three physically equivalent quantization schemes of QCD which are consistent with the decomposition. In particular, we show that the decomposition enlarges the dynamical degrees of QCD by making the topological degrees of the non-Abelian gauge symmetry dynamical. Furthermore with the decomposition we show that the Skyrme-Faddeev theory of non-linear sigma model and QCD have almost identical topological structures. In specific we show that an essential ingredient in both theories is the Wu-Yang type non-Abelian monopole, and that the Faddeev-Niemi knots of the Skyrme-Faddeev theory can actually be interpreted to describe the multiple vacua of the SU (2) QCD. Finally we argue that the Skyrme-Faddeev theory is, just like QCD, a theory of confinement which confines the magnetic flux of the monopoles.
Recently we have obtained a non-perturbative but convergent series expression of the one loop effective action of QED, and discussed the renormalization of the effective action. In this paper we establish the electric-magnetic duality in the quantum effective action.PACS numbers: 11.10.Jj, 11.15.Tk The effective theory of QED plays a crucial role in our understanding of the non-linear effects in electrodynamics. Recently we have obtained a convergent series expression of the effective action of QED in one loop approximation,and established the renormalization group invariance of the effective action [1]. A remarkable feature of the effective action is the electric-magnetic duality,a fundamental symmetry of the quantum effective action of QED. The purpose of this paper is to provide a concrete proof of the duality in the effective action of QED.The effective action of QED has been studied by Euler and Heisenberg and by Schwinger long time ago [2,3],and by many others later [4,5].To derive the effective action one may start from the QED Lagrangianwhere m is the electron mass.With a proper gauge fixing one can show that the electron one loop correction of the effective action is given bySo for an arbitrary constant background one has [2,3] ∆L = − ab 8π 2 ∞+iǫ 0+iǫ dt t coth(at) cot(bt) exp(−m 2 t),
The plant circadian rhythm is quickly entrained to the change of a light stimulus but the mammalian circadian rhythm shows a relatively slow entrainment. Where does such a different entrainment feature of plants and mammals originate? To answer this question, we have investigated circadian regulatory networks of various species and identified the respective core structures of plants and animals. The core circadian regulatory network of plants is composed of two coupled negative feedback loops while the core network of animals consists of coupled negative and positive feedback loops. In addition, the way of regulation (gene transcription or protein degradation) induced by a light stimulus differs depending on species. Mathematical simulations revealed that the topological difference of the core regulatory networks as well as the different way of regulation induced by a light stimulus leads to the different entrainment characteristics of plant and animal circadian clocks.
We consider a brane world residing in the interior region inside the horizon of the D3-brane. The horizon size can be interpreted as the compactification size. The macroscopically large size of extra dimensions then can be derived from the underlying string theory that has only one physical scale, i.e., the string scale. Then, the hierarchy between the string scale and the Planck scale is provided by Ramon-Ramon charge of the D3-brane. This picture also offers a new perspective on various issues associated with the brane world scenarios including the cosmological constant. *
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