A Non-Abelian Variation on the Savvidy Vacuum of the Yang-Mills Gauge Theory

Abstract

As a prelude to a truly non-perturbative 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 non-trivial correlation between the space and color orientations the new background field avoids the possible coordinate singularity, $\mathrm{Det}{B}_i^a=0$, observed recently by Ken Johnson and his collaborators in their Schrödinger 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.

9 pages, preprint BU-HEP-93-22

References in corpus (3)

• The Schrödinger Functional - a Renormalizable Probe for Non-Abelian Gauge Theories
• The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge theory
• Unstable Modes in Three-Dimensional SU(2) Gauge Theory

Cited by in corpus (7)

• Operator Cutoff Regularization and Renormalization Group in Yang-Mills Theory
• A Lattice Simulation of the SU(2) Vacuum Structure
• Quantum stability of non-linear wave type solutions with intrinsic mass parameter in QCD
• Classical Yang Mills equations with sources: consequences of specific scalar potentials
• Kamlah Expansion and Gauge Theories
• Stable Chromomagnetic QCD Vacuum and Confinement
• Vacuum instability by a chromoelectric field in 2 + 1-dimensions