The gluon and quark condensates and their temperature dependence are
investigated within QCD premises. The input for the former is a gauge invariant
gg kernel made up of the direct (D), exchange (X) and contact(C) QCD
interactions in the lowest order, but with the perturbative propagator k−2
replaced by a `non-perturbative k−4 form obtained via two
differentiations: μ2∂m2(m2+k2)−1, (μ a scale
parameter), and then setting m=0, to simulate linear confinement. Similarly
for the input qqˉ kernel the gluon propagator is replaced by the above
k−4 form. With these `linear' simulations, the respective condensates are
obtained by `looping' up the gluon and quark lines in the standard manner.
Using Dimensional regularization (DR), the necessary integrals yield the
condensates plus temperature corrections, with a common scale parameter μ
for both. For gluons the exact result is =36μ4π−3αs(μ2)[2−γ−4π2T2/(3μ2)]. Evaluation
of the quark condensate is preceded by an approximate solution of the SDE for
the mass function m(p), giving a recursive formula, with convergence achieved
at the third iteration. Setting the scale parameter μ equal to the
universal Regge slope 1GeV2, the gluon and quark condensates at T=0 are
found to be 0.586Gev4 and (240−260MeV)3 respectively, in fair accord
with QCD sum rule values. Next, the temperature corrections (of order −T2
for both condensates) is determined via finite-temperature field theory a la
Matsubara. Keywords: Gluon Condensate, mass tensor, gauge invariance, linear
confinement, finite-temperature, contour-closing. PACS: 11.15.Tk ; 12.38.Lg ;
13.20.CzComment: 13 pages (LaTeX) including 2 figure