A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes

The bosonic signature operator is defined for Klein-Gordon fields and massless scalar on globally hyperbolic Lorentzian manifolds of infinite lifetime. construction based an analysis families solutions the equation with a varying mass parameter. It makes use so-called oscillation property which states that integrating over parameter generates decay field at infinity. We derive canonical decomposition solution space into two subspaces, independent observers or choice coordinates. This endows complex structure. also gives rise to distinguished quasi-free state. Taking suitable limit where tends zero, we obtain corresponding results fields. Our constructions are illustrated in examples Minkowski ultrastatic spacetimes.