Universality conditions for the Lorentz invariance of the deconfining phase of the Villain gauge theory

Thesis/Dissertation · Sat Jan 01 04:00:00 EST 1983

OSTI ID:7000438

Gupte, N M

The dimensional Villain gauge theory in the deconfining phase where different orientations of the elementary plaquette carry different weights E/sub ..mu..nu/ is studied. There are thus 6 possible E-s in 4 dimensions. This general theory is interesting because the presence of 6 E-s gives an insight into universality arguments for the Lorentz invariance of 4 dimensional gauge theories. Since the Euclidean formulation is used a discussion of rotational invariance enables conclusions to be drawn about Lorentz invariance. It is not necessary that the field theory be rotationally invariant in the presence of 6 coupling constants E. It may be necessary to impose some condition in the 6 E/sub ..mu..nu/-s to make the theory rotationally invariant. The rotational invariance of the Wilson loop and the plaquette-plaquette correlation function are studied. No conditions on the E/sub ..mu..nu/ are necessary for the rotational invariance of a planar, rectangular Wilson loop oriented parallel to the coodinate axes. However, the plaquette-plaquette correlation function in a plane is not rotationally invariant in the presence of arbitrary E/sub ..mu..nu/. It is necessary to impose the condition E/sub ..mu..nu/ = E/sub ..mu../E/sub nu/ to otain rotational invariance of the plaquette-plaquette correlation function. A 4 parameter subspace of the 6 parameter subspace of the E/sub ..mu..nu/ such that rotational invariance holds in the subspace is found. This has important consequences for existence questions of lattice gauge theories.

• Research Organization: State Univ. of New York, Stony Brook (USA)
• OSTI ID: 7000438
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
INVARIANCE PRINCIPLES
LATTICE FIELD THEORY
LORENTZ INVARIANCE
MATHEMATICAL MODELS
PARTICLE MODELS
QUANTUM FIELD THEORY
ROTATIONAL INVARIANCE
UNIFIED GAUGE MODELS
WILSON LOOP