2013/12/15 by Alexander Stottmeister, Stottmeister, Alexander, Thomas Thiemann +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1312.4173
some typos corrected, extended discussion
openalex publication_date 2013/12/15 · arxiv created 2015/04/09 · arxiv updated 2015/04/10 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
We analyze the implications of the microlocal spectrum/Hadamard condition for states in a (linear) quantum field theory on a globally hyperbolic spacetime M in the context of a (distributional) initial value formulation. More specifically, we work in a 3+1-split M≅ℝ×Σ and give a bound, independent of the spacetime metric, on the wave front sets of the initial data for a quasi-free Hadamard state in the quantum field theory defined by a normally hyperbolic differential operator P acting in a vector bundle E\stackrelπ→M. This aims at a possible way to apply the concept of Hadamard states within approaches to quantum field theory/gravity relying on a Hamiltonian formulation, potentially without a (classical) background metric g.