CHARACTER EXPANSION, ZEROS OF PARTITION-FUNCTION AND THETA-TERM IN U(1) GAUGE-THEORY

Character expansion developed in real space renormalization group (RSRG) approach is applied to U(1) lattice gauge theory with the theta-term in 2 dimensions. The topological charge distribution P(Q) is shown to be of a Gaussian form at any beta (inverse coupling constant). The partition function Z(theta) at large volume is shown to be given by the elliptic theta function. It provides the information of the zeroes of the partition function as an analytic function of zeta = e(i theta) (theta = theta parameter). These partition function zeroes lead to a phase transition at theta = pi. Analytical results will be compared with the MC simulation results. In MC simulation, we adopt (i) ''set method'' and (ii) ''trial function method''.