From Heisenberg-Euler Lagrangian to the discovery of Chromomagnetic Gluon Condensation

by George Savvidy (Demokritos National Research Centre, Athens)

Friday 6 Mar 2020, 13:15 → 14:00 Europe/Stockholm

Fysiska institutionen-Physics Department

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 analyses allows to express the energy momentum tensor, its trace and the vacuum magnetic permeabilities in terms of effective coupling constant and Callan-Symanzik beta function. If the beta function has no zeros, is a negative analytical function of the coupling constant and its integral is finite then it follows that the energy density curve is convex and the minimum of the energy density curve is defined by the extremum where its first derivative vanishes. In the vacuum the energy-momentum tensor is proportional to the space-time metric, and it induces a negative contribution to the effective cosmological constant.