Wilson loops in the light of spin networks. (English) Zbl 1078.81059
Summary: If \(G\) is any finite product of compact orthogonal, unitary and symplectic matrix groups, then Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group \(G\). If \(G\) is orthogonal, unitary or symplectic, then Wilson loops associated to the natural representation of \(G\) are enough.
This extends a result of A. Sengupta [Proc. Am. Math. Soc. 121, No. 3, 897–905 (1994; Zbl 0823.58007)] and earlier work by B. Durhuus [Lett. Math. Phys. 4, No. 6, 515–522 (1980; Zbl 0463.22019)]. In particular, our approach includes the cases of even orthogonal and symplectic groups.
This extends a result of A. Sengupta [Proc. Am. Math. Soc. 121, No. 3, 897–905 (1994; Zbl 0823.58007)] and earlier work by B. Durhuus [Lett. Math. Phys. 4, No. 6, 515–522 (1980; Zbl 0463.22019)]. In particular, our approach includes the cases of even orthogonal and symplectic groups.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 20C35 | Applications of group representations to physics and other areas of science |
| 53C80 | Applications of global differential geometry to the sciences |
References:
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