Local incompatibility of the microlocal spectrum condition with the KMS property along spacelike directions in quantum field theory on curved spacetime

Abstract

States of a generic quantum field theory on a curved spacetime are considered, which satisfy the KMS condition with respect to an evolution associated with a complete (Killing) vector field. It is shown that at any point where the vector field is spacelike, such states cannot satisfy a certain microlocal regularity condition, which is weaker than the microlocal spectrum condition in the case of asymptotically free fields.

The Unruh state for massless fermions on Kerr spacetime and its Hadamard property

“…(2) A theorem due to Pinamonti-Sanders-Verch asserts that a thermal state associated with a complete Killing vector field v cannot be Hadamard if there is a point at which v is space-like [50]. This result holds true in a broad setting including bosonic and fermionic non-interacting fields.…”