2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53566The chiral phase dependence of fermion partition function in spherically symmetric U(1) gauge field background is analyzed in two dimensional space-time. A well-defined method to calculated the path integral which apply to the continuous fermion spectrum is described. The one-to-one correspondence between the nonzero energy continuous spectra of two pertinent hamiltonians, which are defined by the Dirac operator to make the path integral well-defined, is shown to be exact. The asymptotic expansion for the chiral phase dependence in \(1/|m|^2\) (\(m\) is mass of the fermion.) is proposed and the coefficients in the expansion are evaluated up to the next-to-next leading term. Up to this order, the chiral phase dependence is given only by the winding number of background field and the corrections vanish.29 page (LaTeX) + 1 figure (figure is available upon request.), UCRHEP-T110High Energy Physics - Theorytext