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Multi-hadron operators are crucial for reliably extracting the masses ofexcited states lying above multi-hadron thresholds in lattice QCD Monte Carlocalculations. The construction of multi-hadron operators with significantcoupling to the lowest-lying multi-hadron states of interest involves combiningsingle hadron operators of various momenta. The design and implementation oflarge sets of spatially-extended single-hadron operators of definite momentumand their combinations into two-hadron operators are described. The singlehadron operators are all assemblages of gauge-covariantly-displaced, smearedquark fields. Group-theoretical projections onto the irreduciblerepresentations of the symmetry group of a cubic spatial lattice are used inall isospin channels. Tests of these operators on 24^3 x 128 and 32^3 x 256anisotropic lattices using a stochastic method of treating the low-lying modesof quark propagation which exploits Laplacian Heaviside quark-field smearingare presented. The method provides reliable estimates of all neededcorrelations, even those that are particularly difficult to compute, such aseta eta -> eta eta in the scalar channel, which involves the subtraction of alarge vacuum expectation value. A new glueball operator is introduced, and theevaluation of the mixing of this glueball operator with a quark-antiquarkoperator, pi-pi, and eta-eta operators is shown to be feasible.

Extended hadron and two-hadron operators of definite momentum for spectrum calculations in lattice QCD