Sz. Huang et Ar. Levi, NON-ABELIAN VARIATION ON THE SAVVIDY VACUUM OF THE YANG-MILLS GAUGE-THEORY, Physical review. D. Particles and fields, 49(12), 1994, pp. 6849-6856
As a prelude to a truly nonperturbative evaluation of the effective po
tential in terms of lattice QCD, the one loop effective potential for
a non-Abelian gauge.configuration is calculated using the background f
ield method. Through a nontrivial correlation between the space and co
lor orientations the new background field avoids the possible coordina
te singularity, DetB(i)a = 0, observed recently by Johnson and his col
laborators in their Schrodinger functional study of the SU(2) Yang-Mil
ls theory. In addition, since our ansatz generates a constant color ma
gnetic field through the commutator terms rather than derivative terms
, many of the technical drawbacks the Savvidy ansatz suffers on a latt
ice can be avoided. Our one loop study yields qualitatively the same r
esult as that of Savvidy's. In particular, the main difficulty of the
loop expansion in the presence of a constant chromomagnetic background
field, i.e., the appearance of the imaginary part in the effective po
tential, is not removed by avoiding the singularity of DetB(i)a = 0.