Quantum Back Reaction on a Classical Field

Abstract

We show how to apply post selection in the context of weak measurement of Aharonov and collaborators to construct the quantum back reaction on a classical field. The particular case which we study in this paper is pair creation in an external electric field and the back reaction is the counter field produced by the pair \underline {as} it is made. The construction leads to a complex electric field obtained from non diagonal matrix elements of the current operator, the interpretation of which is clear in terms of weak measurement. The analogous construction applied to black hole physics (thereby leading to a complex metric) is relegated to a future paper.