NON-ABELIAN VARIATION ON THE SAVVIDY VACUUM OF THE YANG-MILLS GAUGE-THEORY

As a prelude to a truly nonperturbative evaluation of the effective potential in terms of lattice QCD, the one loop effective potential for a non-Abelian gauge.configuration is calculated using the background field method. Through a nontrivial correlation between the space and color orientations the new background field avoids the possible coordinate singularity, DetB(i)a = 0, observed recently by Johnson and his collaborators in their Schrodinger functional study of the SU(2) Yang-Mills theory. In addition, since our ansatz generates a constant color magnetic field through the commutator terms rather than derivative terms, many of the technical drawbacks the Savvidy ansatz suffers on a lattice can be avoided. Our one loop study yields qualitatively the same result 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 potential, is not removed by avoiding the singularity of DetB(i)a = 0.