Generalized Coherent States and Random Shift Operators

We study the Chernoff averages for random generalized shift operators in the case of noncanonical commutation relations between creation and annihilation operators. We introduce the concepts of shift-dual ladder operators and generalized shift operators. As an example, we consider a one-parameter family of commutation relations for which generalized shift operators are unitary and satisfy the semigroup property on straight lines passing through the origin. For this family, we prove that the sequence of expectations of Feynman–Chernoff iterations of random shift operators converges to a limit strongly continuous semigroup.