Universality conditions for the Lorentz invariance of the deconfining phase of the Villain gauge theory
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
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
UNIFIED GAUGE MODELS
LORENTZ INVARIANCE
FOUR-DIMENSIONAL CALCULATIONS
LATTICE FIELD THEORY
ROTATIONAL INVARIANCE
WILSON LOOP
FIELD THEORIES
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
PARTICLE MODELS
QUANTUM FIELD THEORY
645400* - High Energy Physics- Field Theory