FERMION FIELD ON RANDOM LATTICES

The problem of formulating the chiral fermion field on space-time latt ices is discussed from the viewpoint of functional integrals. We argue that the functional integral measure provided by any single lattice i s not sufficent to yield solutions to agree with the continuum field t heory. The approaches of using an ensemble of random-block lattices (R BL) as well as CFL random lattices to provide a proper functional inte gral measure are investigated. For a massless fermion field interactin g with a background abelian gauge field in 2D, the RBL randomization g ives results in very good agreement with the continuum field theory, w hile the CFL randomization fails to yield the correct axial-vector cur rent and axial anomaly.