The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons and the colored valence gluons shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the valence gluons as colored source, and simplifies the QCD dynamics greatly. In particular, it tells that the gauge covariant valence gluons can be treated as the constituents of hadrons, and generalizes the quark model to the quark and valence gluon model. So it provides a comprehensive picture of glueballs and their mixing with quarkoniums, and predicts new hybrid hadrons made of quarks and valence gluons. We discuss how these predictions could be confirmed experimentally. In particular we present a systematic search for the ground state glueballs and their mixing with quarkoniums below 2 GeV in 0 ++ , 2 ++ , and 0 −+ channels within the framework of QCD, and predict the relative branching ratios of the radiative decay of ψ to the physical states.

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.

The latest MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss three different ways to estimate the mass of the electroweak monopole. We first present the dimensional and scaling arguments which indicate the monopole mass to be around 4 to 10 TeV . To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strength at short distance. Our result demonstrates that a genuine electroweak monopole whose mass scale is much smaller than the grand unification scale can exist, which can actually be detected at the present LHC.

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We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation that is responsible for the confinement. To demonstrate this we present a new gauge-invariant integral expression of the one-loop QCD effective action which has no infrared divergence. With this we show that, just as the GliozziScherk-Olive projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance (''the C projection'') assures the gauge invariance and the stability of the monopole condensation. This establishes the monopole dominance in QCD. In doing so we point out critical defects in the calculation of the Savvidy-Nielsen-Olesen effective action.

We demonstrate the monopole condensation in SU(3) QCD. We first discuss the gauge independent and Weyl symmetric Abelian (Cho-Duan-Ge) decomposition of the SU(3) QCD, and present a new gauge invariant integral expression of the one-loop effective action which has no infrared divergence. Integrating it gauge invariantly imposing the color reflection invariance ("the C-projection") we show that the effective potential generates the stable monopole condensation which generates the mass gap.

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),

A new Lorentz gauge gravity model with R 2 -type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space-time background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin two mode of torsion becomes dynamical essentially due to the non-linear structure of the theory. We perform covariant one-loop quantization of the model for a special case of constant curvature space-time background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced due to quantum dynamics of torsion.