Quantum electrodynamics on the lattice and numerical perturbative computation of g-2

We compute the electron g factor to the O(alpha(5)) order on the lattice in quenched quantum electrodynamics (QED). We first study finite volume (FV) corrections in various infrared regularization methods to discuss which regularization is optimal for our purpose. We find that in QED(L) the FV correction to the effective mass can have different parametric dependences depending on the size of Euclidean time t and match the 'naive on-shell result' only at the very large t region, t >> L . We adopt finite photon mass regularization to suppress FV effects exponentially and also discuss our strategy for selecting simulation parameters and the order of extrapolations to efficiently obtain the g factor. We perform lattice simulation using small lattices to test the feasibility of our calculation strategy. This study can be regarded as an intermediate step toward giving the five-loop coefficient independently of preceding studies.