Classical response theory in the Heisenberg picture

Abstract
A new derivation of classical response theory is presented from the Heisenberg point of view, where observable properties are followed along a classical many-body trajectory. The exact equivalence of the Heisenberg (observable) and Schrödinger (distribution function) pictures is shown and the nature of their relationship is clarified. The formal expression is derived for the response to time-dependent external fields, to all orders.