2013/07/31 by Christopher J Fewster, Rainer Verch · 2 citations
Mathematics · Physics and Astronomy · #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/30/23/235027
published as Class. Quantum Grav. 30 (2013) 235027 · v2 24pp typos fixed, references added
arxiv created 2013/08/08 · arxiv updated 2016/08/29
Hadamard states are generally considered as the physical states for linear quantized fields on curved spacetimes, for several good reasons. Here, we provide a new motivation for the Hadamard condition: for "ultrastatic slab spacetimes" with compact Cauchy surface, we show that the Wick squares of all time derivatives of the quantized Klein-Gordon field have finite fluctuations only if the Wick-ordering is defined with respect to a Hadamard state. This provides a converse to an important result of Brunetti and Fredenhagen. The recently proposed "S-J (Sorkin-Johnston) states" are shown, generically, to give infinite fluctuations for the Wick square of the time derivative of the field, further limiting their utility as reasonable states. Motivated by the S-J construction, we also study the general question of extending states that are pure (or given by density matrices relative to a pure state) on a double-cone region of Minkowski space. We prove a result for general quantum field theories showing that such states cannot be extended to any larger double-cone without encountering singular behaviour at the spacelike boundary of the inner region. In the context of the Klein-Gordon field this shows that even if an S-J state is Hadamard within the double cone, this must fail at the boundary.