Abstract
We study Abelian lattice gauge theory defined on a simplicial complex with arbitrary topology. The use of dual objects allows one to reformulate the theory in terms of different dynamical variables; however, we avoid entirely the use of the dual cell complex. Topological modes which are present in the transformation now appear as homology classes, in contrast to the cohomology modes found in the dual cell picture. Irregularities of dual cell complexes do not arise in this approach. We treat the two and three-dimensional cases in detail, and prove a general vanishing theorem for Wilson line correlators.
Similar content being viewed by others
References
Kramers, H. and Wannier, G.: Phys. Rev. 60 (1941), 252.
Savit, R.: Duality in field theory and statistical systems, Rev. Modern Phys. 52 (1980), 453-487.
Drühl, K. and Wagner, H.: Algebraic formulation of duality transformations for Abelian lattice models, Ann. of Phys. 141 (1982), 225-253.
Rakowski, M.: Topological modes in dual lattice models, Phys. Rev. D 52 (1995), 354-357.
Munkres, J.: Elements of Algebraic Topology, Addison-Wesley, Menlo Park, 1984.
Creutz, M.: Quarks, Gluons and Lattices, Cambridge Univ. Press, Cambridge, 1985.
Migdal, A.: Zh. Eksper. Teoret. Fiz. 69 (1975), 810 (Soviet Phys. JETP 42, 413).
Witten, E.: On quantum gauge theories in two dimensions, Comm. Math. Phys. 141 (1991), 153-209.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rakowski, M., Sen, S. Homology in Abelian Lattice Models. Letters in Mathematical Physics 42, 195–204 (1997). https://doi.org/10.1023/A:1007355709831
Issue Date:
DOI: https://doi.org/10.1023/A:1007355709831