2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/54295Definition of the determinant of Euclidean Dirac operator in the nontrivial sector of gauge fields suffers from an inherent ambiguity. The popular Osterwalder-Schrader (OS) recipe for the conjugate Dirac field leads to the option of a vanishing determinant. We propose a novel representation for the conjugate field which depends linearly on the Dirac field and yields a nonvanishing determinant in the nontrivial sector. Physics, it appears, chooses this second option becuase the novel representation leads to a satisfactory resolution of two outstanding problems, the strong CP and U(1) problems, attributed to instanton effects.Latex file, 9 pages, no figureHigh Energy Physics - Theorytext