Abelian Decomposition and Monopole Condensation in QCD

Abstract

We demonstrate the monopole condensation in QCD using the Abelian decomposition. The Abelian decomposition decomposes the gluons to the color neutral binding gluons (the neurons and the monopoles) and the colored valence gluons (the chromons), and shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the chromons as colored source. This simplifies the QCD dynamics greatly. In the perturbative regime this decomposes the gluon propagater to the neuron propagaters and the chromon propagaters, and simplifies the Feynman diagram. In the non-perturbative regime this allows us to calculate the QCD effective potential gauge independently, and demonstrate the monopole condensation unambiguously.