Dynamical Fermion on Random-Block Lattice

The problem of formulating the chiral fermion field on space-time lattices has been discussed from the viewpoint of funtional integrals [1]. I argued that the functional integral measure provided by any single lattice ( hypercubical lattice or random lattice ) is not sufficent to yield fermionic functional integrals to agree with the continuum field theory. My proposal of using an ensemble of random-block lattices ( RBL ) to provide a proper measure has been investigated. RBL regularization has been tested for the free fermion ( massive and massless ) in 2d and 4d [2,3] respectively, and for 2d massless fermion in an external abelian gauge field [4,5]. All observables including fermion propagators, gauge invariant currents, axial anomaly and current-current correlations are all in good agreement with the continuum field theory. It is natural for us to proceed to investigations involving dynamical fermion field on RBL. In this paper, massless fermion field interacting with the dynamical abelian gauge field on 2d RBL is studied. Using Hybrid Monte Carlo simulations, the Wilson loop and the chiral correlation function are measured and preliminary results of these observables are in agreement with the continuum Schwinger model. More extensive measurements involving higher statistics and larger lattices are now in progress and will be reported elsewhere.