A consistent approach to Hamiltonian SU(N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriate chosen set of angular variables. The various constraints are carefully discussed, as is a practical means for their implementation. A complete set of variables for the colourless sector is thereby determined. We show that the one-plaquette problem in SU(N) gauge theory can be mapped onto a problem of N fermions on a torus, which is solved numerically for the low-lying energy spectra for N<6. We end with a brief discussion of how to entend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster parametrisation of the full wave functional.
|Title of host publication||Proceedings of the 13th International Conference on Recent Progress in Many-Body Theories|
|Place of Publication||Singapore|
|Number of pages||16|
|Publication status||Published - Sep 2006|
|Name||Series on Advances in Quantum Many-Body Theory|
Bishop, R. F., Ligterink, N. E., & Walet, N. R. (2006). Towards the coupled-cluster treatment of SU(N) lattice gauge field theory. In Proceedings of the 13th International Conference on Recent Progress in Many-Body Theories (pp. 22-38). (Series on Advances in Quantum Many-Body Theory; Vol. 10, No. 500-266). Singapore: World Scientific.