Vacuum Energy Density in the Quantum Yang - Mills Theory

Abstract

Using the effective potential approach for composite operators, we have formulated a general method of calculation of the truly non-perturbative Yang-Mills vacuum energy density (this is, by definition, the Bag constant apart from the sign). It is the main dynamical characteristic of the QCD ground state. Our method allows one to make it free of the perturbative contributions ('contaminations'), by construction. We also perform an actual numerical calculation of the Bag constant for the confining effective charge. Its choice uniquely defines the Bag constant, which becomes free of all the types of the perturbative contributions now, as well as possessing many other desirable properties as colorless, gauge independence, etc. Using further the trace anomaly relation, we develop a general formalism which makes it possible to relate the Bag constant to the gluon condensate not using the weak coupling solution for the corresponding $\beta$ function. Our numerical result for the Bag constant shows a good agreement with other phenomenological estimates of the gluon condensate.

28 pages and 4 figures, typos corrected, added new appendices and new references in comparison with the published version

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Cited by in corpus (4)

• The non-perturbative analytical equation of state for the gluon matter. I
• Influence of light quark loops on the Wigner phase with Dyson-Schwinger equations approach
• A New Strategy For Solving Two Cosmological Problems in Hadron Physics
• A New Interpretation of Einstein's Cosmological Constant