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Recent Progress in Many-Body Theories

TOWARDS A COUPLED-CLUSTER TREATMENT OF SU (N) LATTICE GAUGE FIELD THEORY

R. F. Bishop, N.E. Ligterink, Niels R. Walet

Published Sep 1, 2006• 0 citations
Publisher
DOI
10.1142/9789812772787_0003

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TOWARDS A COUPLED-CLUSTER TREATMENT OF SU (N) LATTICE GAUGE FIELD THEORY

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A consistent approach to Hamiltonian SU (N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately 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 ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional.

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A consistent approach to Hamiltonian SU (N) lattice gauge field theory is developed using the maximal-tree gauge and an appropriately 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 ≤ 5. We end with a brief discussion of how to extend the approach to include the spatial (inter-plaquette) correlations of the full theory, by using a coupled-cluster method parametrisation of the full wave functional.