2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167935The transition amplitude between square roots of states, which is an analogue of Hellinger integral in classical measure theory, is investigated in connection with operator-algebraic representation theory. A variational expression based on geometric mean of positive forms is utilized to obtain an approximation formula for transition amplitudes.12pagesMathematical PhysicsOperator Algebras46L60; 46L53text