Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1992-12-18
Phys.Lett. B302 (1993) 463-471
Physics
High Energy Physics
High Energy Physics - Lattice
13 pages + 5 postscript figures, plain Latex
Scientific paper
10.1016/0370-2693(93)90428-K
It is shown how to adapt the non-perturbative coupled cluster method of many-body theory so that it may be successfully applied to Hamiltonian lattice $SU(N)$ gauge theories. The procedure involves first writing the wavefunctions for the vacuum and excited states in terms of linked clusters of gauge invariant excitations of the strong coupling vacuum. The fundamental approximation scheme then consists of i) a truncation of the infinite set of clusters in the wavefunctions according to their geometric {\em size}, with all larger clusters appearing in the Schr\"odinger equations simply discarded, ii) an expansion of the truncated wavefunctions in terms of the remaining clusters rearranged, or ``shifted'', to describe gauge invariant {\em fluctuations} about their vacuum expectation values. The resulting non-linear truncated Schr\"odinger equations are then solved self-consistently and exactly. Results are presented for the case of $SU(2)$ in $d=3$ space-time dimensions.
Llewellyn Smith C. H.
Watson N. J.
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