Effective transfer matrix for low-lying glueball states in lattice gauge theory

Abstract

In four-dimensional lattice gauge theory without quarks the lowest particle states in the strong coupling region correspond to a spin-zero and a spin-two glueball. They are degenerate in the lowest order of the strong coupling expansion. There exists an effective transfer matrix, acting in the lowest order eigenspace, whose eigenvalues are identical with the corresponding ones of the full transfer matrix to all orders in the strong coupling expansion. It is constructed here up to the eighth nontrivial order for different gauge groups. Diagonalization yields the energy-momentum dispersion relations for glueball states.