Non-Abelian variation on the Savvidy vacuum of the Yang-Mills gauge theory
- 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)
- 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), Vol. 49:12; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
QUANTUM CHROMODYNAMICS
LATTICE FIELD THEORY
YANG-MILLS THEORY
VACUUM STATES
COLOR
COMMUTATORS
CORRELATIONS
MAGNETIC FIELDS
POTENTIALS
SINGULARITY
SU-2 GROUPS
FIELD THEORIES
LIE GROUPS
MATHEMATICAL OPERATORS
OPTICAL PROPERTIES
ORGANOLEPTIC PROPERTIES
PHYSICAL PROPERTIES
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SU GROUPS
SYMMETRY GROUPS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
662230 - Quantum Chromodynamics- (1992-)