From Heisenberg-Euler Lagrangian to the discovery of chromomagnetic gluon condensation

Abstract

I reexamine the phenomena of the chromomagnetic gluon condensation in Yang-Mills theory. The extension of the Heisenberg-Euler Lagrangian to the Yang-Mills theory allows to calculate the effective action, the energy-momentum tensor and demonstrate that the energy density curve crosses the zero energy level of the perturbative vacuum state at nonzero angle and continuously enters to the negative energy density region. At the crossing point and further down the effective coupling constant is small and demonstrate that the true vacuum state of the Yang-Mills theory is below the perturbative vacuum state and is described by the nonzero chromomagnetic gluon condensate. The renormalisation group analysis allows to express the energy momentum tensor, its trace and the first and second order derivatives in terms of Callan-Symanzik beta function and effective coupling constant. The derivatives define the convexity and the extremum of the energy density curve. In the vacuum the energy-momentum tensor is proportional to the space-time metric, and induces a negative contribution to the effective cosmological constant.