Semiclassical analysis of the weak-coupling limit of SU(2) lattice gauge theory: The extreme infrared region

1990 ◽  
Vol 42 (4) ◽  
pp. 1233-1245 ◽  
Author(s):  
Jochen Bartels ◽  
Bernd Raabe ◽  
Tai Tsun Wu
Keyword(s):  
Gauge Theory ◽  
Weak Coupling ◽  
Lattice Gauge Theory ◽  
Infrared Region ◽  
Weak Coupling Limit ◽  
Semiclassical Analysis ◽  
Lattice Gauge

scholarly journals q-DEFORMED LATTICE GAUGE THEORY AND 3-MANIFOLD INVARIANTS

1993 ◽  
Vol 08 (18) ◽  
pp. 3139-3162 ◽  
Author(s):  
D. V. BOULATOV
Keyword(s):  
Gauge Theory ◽  
Weak Coupling ◽  
Deformation Parameter ◽  
Lattice Gauge Theory ◽  
Universal Covering ◽  
Weak Coupling Limit ◽  
Topological Invariant ◽  
Cell Complexes ◽  
Root Of Unity ◽  
Lattice Gauge

The notion of q-deformed lattice gauge theory is introduced. If the deformation parameter is a root of unity, the weak coupling limit of a 3-d partition function gives a topological invariant of a corresponding 3-manifold. It enables us to define the generalized Turaev–Viro invariant for cell complexes. It is shown that this invariant is determined by an action of a fundamental group on a universal covering of a complex. A connection with invariants of framed links in a manifold is also explored. A model giving a generating function of all simplicial complexes weighted with the invariant is investigated.

Boundary conditions, gauge fixing ambiguities and exact expectation values in U(1) lattice gauge theory

2016 ◽  
Vol 31 (08) ◽  
pp. 1650035
Author(s):  
Carlos Pinto
Keyword(s):  
Gauge Theory ◽  
Boundary Conditions ◽  
Weak Coupling ◽  
Lattice Gauge Theory ◽  
Exact Results ◽  
Feynman Gauge ◽  
Lattice Gauge ◽  
Coupling Approximation ◽  
Gauge Fixing ◽  
Weak Coupling Approximation

We analyze the interplay between gauge fixing and boundary conditions in two-dimensional U(1) lattice gauge theory. We show on the basis of a general argument that periodic boundary conditions result in an ill-defined weak coupling approximation but that the approximation can be made well-defined if the boundaries are fixed to zero. We confirm this result in the particular case of the Feynman gauge. We show that the zero momentum mode divergence in the propagator that appears in the Feynman gauge vanishes when the weak coupling approximation is well-defined. In addition we obtain exact results (for arbitrary coupling), including finite size corrections, for the partition function and for general one-point and two-point functions in the axial gauge under both periodic and zero boundary conditions and confirm these results numerically. The dependence of these objects on both lattice size and coupling constant is investigated using specific examples. These exact results may provide insight into similar gauge fixing issues in more complex models.

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