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

Character expansion developed in real space renormalization group (RSR G) approach is applied to U(1) lattice gauge theory with the theta-ter m in 2 dimensions. The topological charge distribution P(Q) is shown t o be of a Gaussian form at any beta (inverse coupling constant). The p artition 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 ph ase transition at theta = pi. Analytical results will be compared with the MC simulation results. In MC simulation, we adopt (i) ''set metho d'' and (ii) ''trial function method''.