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 analyses allows to express the energy momentum tensor, its trace and the vacuum magnetic permeabilities in QED and QCD in terms of effective coupling constant and Callan–Symanzik beta function. 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.
Highlights
In this article we shall analyse the effective action in QED and QCD by using the perturbative loop expansion and renormalisation group equations and discuss the physical consequences which can be derived from their explicit expressions
It is conjectured that the quantum vacua of the “Mirror SM” contribute to the cosmological constant on the same footing as the SM, since mirror particles are expected to gravitate in the same way as the usual ones, and that the mirror chromoelectric gluon condensate contributes to the energy density of the universe with a positive sign and may, in principle, eliminates the negative QCD vacuum effect by yielding a cosmological constant small
One can consider the above approach of calculating the effective action as an alternative to a standard loop expansion in the following sense: The expansion is organised by rearranging the perturbative expansion (5.1) in a background field A so that the quartic self-interactions of eigenmodes are included into the propagator of the gauge field G(x, y; A) and the loop expansion is performed in terms of the remaining cubic and cross-mode quartic vertices of the YM action
Summary
In this article we shall analyse the effective action in QED and QCD by using the perturbative loop expansion and renormalisation group equations and discuss the physical consequences which can be derived from their explicit expressions. To calculate the energy momentum tensor Tμν in pure SU (N ) YM theory one should use the expression (1.4) and in the case of QCD, in the limit of chiral fermions, one should add the quark contribution (1.5) by using the substitution 11N → b = 11N − 2N f : Tμν = TμYνM. Substituting the vacuum field intensity (1.15) into the expression for the energy momentum tensor (1.13) one can get that in the vacuum the tensor Tμν is proportional to the space-time metric gμν: Tμν vac = −gμν b 96π 2 In this form the energy momentum tensor represents the relativistically invariant equation of state vac = −Pvac, which uniquely characterises the vacuum [17,18,19,20] with its negative energy density vac. One can calculate different observables of physical interest that will include the effective energy momentum tensor, vacuum energy density, the magnetic permeability, the effective coupling constants and their behaviour as a function of the external fields. The energy density curve (F) (1.14) intersect the horizontal zero energy line at the nonzero angle θ > 0
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