Non-Abelian variation on the Savvidy vacuum of the Yang-Mills gauge theory

Journal Article · Wed Jun 15 00:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.49.6849· OSTI ID:7308581

Huang, S ^[1]; Levi, A R ^[2]

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1. Department of Physics, FM-15, University of Washington, Seattle, Washington 98195 (United States) Center for Theoretical Physics, Laboratory for Nuclear Science, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
2. Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215 (United States)

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, Det[ital B][sub [ital i]][sup [ital a]]=0, observed recently by Johnson and his collaborators in their Schroedinger 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 Det[ital B][sub [ital i]][sup [ital a]]=0.

• DOE Contract Number: FG06-88ER40427; AC02-76ER03069; FG02-91ER40676
• OSTI ID: 7308581
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 49:12; ISSN 0556-2821; ISSN PRVDAQ
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
662230 -- Quantum Chromodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COLOR
COMMUTATORS
CORRELATIONS
FIELD THEORIES
LATTICE FIELD THEORY
LIE GROUPS
MAGNETIC FIELDS
MATHEMATICAL OPERATORS
OPTICAL PROPERTIES
ORGANOLEPTIC PROPERTIES
PHYSICAL PROPERTIES
POTENTIALS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SINGULARITY
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
VACUUM STATES
YANG-MILLS THEORY