2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/39067U(2) lattice gauge theory with $θ$-term in 2 space-time dimensions is investigated. It has non-Abelian real action and Abelian( U(1) type) imaginary action. The imaginary action is defined as the standard $θ$-term. As the effect of renormalization group (RG) transformation, non-Abelian imaginary action is induced. After many steps of RG transformation, non-Abelian part will die away. After several steps of RG transformations, renormalized action approaches so called heat kernel action. Phase transition is found at $θ=π$ only.Plain tex, 20pages with 10figuresHigh Energy Physics - Latticetext