The Coupled Cluster Method in Hamiltonian Lattice Field Theory

The coupled cluster or exp S form of the eigenvalue problem for lattice Hamiltonian QCD (without quarks) is investigated. A new construction prescription is given for the calculation of the relevant coupled cluster matrix elements with respect to an orthogonal and independent loop space basis. The method avoids the explicit introduction of gauge group coupling coefficients by mapping the eigenvalue problem onto a suitable set of character functions, which allows a simplified procedure. Using appropriate group theoretical methods, we show that it is possible to set up the eigenvalue problem for eigenstates having arbitrary lattice momentum and lattice angular momentum.Comment: LaTeX, no figur

The Collective Field Theory of a Singular Supersymmetric Matrix Model

The supersymmetric collective field theory with the potential $v'(x)=\omega x-{\eta\over x}$ is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeros of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a majorana fermion. The $x$ space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.Comment: Revtex 8 pages, Submitted to Phys. Rev. D. References and preprint numbers have been adde

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange