The monograph is devoted to in-depth analysis of the Langrangian approach in momentum picture of motion to quantum free scalar, spinor and vector fields. The main purpose of the monograph is to suggest a new approach and analysis of known of problems which results in reestablishment of known facts and new results. Almost all considerations will be done in the momentum picture of motion instead of the standard representation in Heisenberg picture of motion. All calculations are given in full details and the hypotheses underlying the theory are explicitly formulated at the points when they are logically required.