Real Space Renormalization Group Analysis of U(1)-Gauge Theory with Term in 2 Dimensions

U(1) lattice gauge theory with $\theta$-term is investigated by real spacerenormalization group approach. Flows of renormalized coupling constants areanalyzed. For each $\theta$, renormalization flows converge to a singletrajectory irrespective of bare coupling constants of real action. For $\theta\not= \pi$ the system is in the confinement phase controlled by an infraredfixed point. We found a phase transition at $\theta = \pi$. Imaginary part ofthe action given by $\theta$-term stays fixed under renormalization grouptransformations leading to deconfinement.Comment: plaintex 14 pages and 9 figures,( Figures will be sent upon request.