TY - JOUR
T1 - Topological interpretations of lattice gauge field theory
AU - Bullock, Doug
AU - Frohman, Charles
AU - Kania-Bartoszyńska, Joanna
PY - 1998
Y1 - 1998
N2 - We construct lattice gauge field theory based on a quantum group on a lattice of dimension one. Innovations include a coalgebra structure on the connections and an investigation of connections that are not distinguishable by observables. We prove that when the quantum group is a deformation of a connected algebraic group G (over the complex numbers), then the algebra of observables forms a deformation quantization of the ring of G-characters of the fundamental group of the lattice. Finally, we investigate lattice gauge field theory based on quantum SL2ℂ, and conclude that the algebra of observables is the Kauffman bracket skein module of a cylinder over a surface associated to the lattice.
AB - We construct lattice gauge field theory based on a quantum group on a lattice of dimension one. Innovations include a coalgebra structure on the connections and an investigation of connections that are not distinguishable by observables. We prove that when the quantum group is a deformation of a connected algebraic group G (over the complex numbers), then the algebra of observables forms a deformation quantization of the ring of G-characters of the fundamental group of the lattice. Finally, we investigate lattice gauge field theory based on quantum SL2ℂ, and conclude that the algebra of observables is the Kauffman bracket skein module of a cylinder over a surface associated to the lattice.
UR - http://www.scopus.com/inward/record.url?scp=0032210256&partnerID=8YFLogxK
U2 - 10.1007/s002200050471
DO - 10.1007/s002200050471
M3 - Article
AN - SCOPUS:0032210256
SN - 0010-3616
VL - 198
SP - 47
EP - 81
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 1
ER -