Vortex operators in gauge field theories
Several related aspects of the 't Hooft vortex operator are studied. The current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator are reviewed first. The Abelian vortex operator written in terms of elementary fields and the calculation of its Green's functions are considered. A two-dimensional solvable model of a Dirac string is presented. The expression of the Green's functions more neatly in terms of Wu and Yang's geometrical idea of sections is addressed. The renormalization of the Green's functions of two kinds of Abelian looplike operators, the Wilson loop and the vortex operator, is studied; for both operators only an overall multiplicative renormalization is needed. In the case of the vortex this involves a surprising cancellation. Next, the dependence of the Green's functions of the Wilson and 't Hooft operators on the nature of the vacuum is discussed. The cluster properties of the Green's functions are emphasized. It is seen that the vortex operator in a massive Abelian theory always has surface-like clustering. The form of Green's functions in terms of Feynman graphs is the same in Higgs and symmetric phases; the difference appears in the sum over all tadpole trees. Finally, systems having fields in the fundamental representation are considered. When these fields enter only weakly into the dynamics, a vortex-like operator is anticipated. Any such operator can no longer be local looplike, but must have commutators at long range. A U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint), is examined. When the fundamental field is weakly coupled, the expected phase transitions are found. When it is strongly coupled, the operator still appears to be a good order parameter, a discontinuous change in its behavior leads to a new phase transition. 18 figures.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5055719
- Report Number(s):
- LBL-11295; TRN: 80-015745
- Resource Relation:
- Other Information: Thesis
- Country of Publication:
- United States
- Language:
- English
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QUANTUM FIELD THEORY
QUANTUM OPERATORS
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LATTICE FIELD THEORY
PHASE TRANSFORMATIONS
QUANTUM CHROMODYNAMICS
RENORMALIZATION
STRING MODELS
VACUUM STATES
VORTICES
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
FIELD THEORIES
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
PARTICLE MODELS
QUARK MODEL
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