Complex Structures for Klein-Gordon Theory on Globally Hyperbolic Spacetimes

Albert Much, Robert Oeckl

Published 2018-12-03Version 1

We develop a rigorous method to parametrize conserved complex structures for Klein-Gordon theory in globally hyperbolic spacetimes that admit complete Cauchy surfaces. The complex structures implement unitary quantizations and can be interpreted as corresponding to choices of vacuum. The main ingredient in our construction is a system of operator differential equations. We provide a number of theorems ensuring that all ingredients and steps in the construction are well-defined. We apply the method to exhibit natural quantizations for certain classes of globally hyperbolic spacetimes. In particular, we consider static, expanding and Friedmann-Robertson-Walker spacetimes.