Feynman formulas for qp- and pq-quantization of some Vladimirov type time-dependent Hamiltonians on finite adeles.

Let Q be the d-dimensional space of finite adeles over the algebraic number field K and let P = Q ∗ be its dual space. For a certain type of Vladimirov type time-dependent Hamiltonian H V (t) : Q × P → C we construct the Feynman formulas for the solution of the Cauchy problem with the Schrödinger operator where the caret operator stands for the qp- or pq-quantization. [ABSTRACT FROM AUTHOR]