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^* P=Q∗ be its dual space. For a certain type of Vladimirov type time-dependent Hamiltonian HV(t):Q× P→ C HV(t):Q×P→C we construct the Feynman formulas for the solution of the Cauchy problem with the Schrödinger operator "Equation missing"where the caret operator stands for the qp - or pq -quantization.