@article{Lewandowski2022,
  author    = {Lewandowski, Max},
  title     = {Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes},
  series = {Journal of mathematical physics},
  volume    = {63},
  journal   = {Journal of mathematical physics},
  number    = {1},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0022-2488},
  doi       = {10.1063/5.0055753},
  pages     = {34},
  year      = {2022},
  abstract  = {According to Radzikowski's celebrated results, bisolutions of a wave operator on a globally hyperbolic spacetime are of the Hadamard form iff they are given by a linear combination of distinguished parametrices i2(G˜aF-G˜F+G˜A-G˜R) in the sense of Duistermaat and H{\"o}rmander [Acta Math. 128, 183-269 (1972)] and Radzikowski [Commun. Math. Phys. 179, 529 (1996)]. Inspired by the construction of the corresponding advanced and retarded Green operator GA, GR as done by B{\"a}r, Ginoux, and Pf{\"a}ffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Z{\"u}rich, 2007]}, we construct the remaining two Green operators GF, GaF locally in terms of Hadamard series. Afterward, we provide the global construction of i2(G˜aF-G˜F), which relies on new techniques such as a well-posed Cauchy problem for bisolutions and a patching argument using Čech cohomology. This leads to global bisolutions of the Hadamard form, each of which can be chosen to be a Hadamard two-point-function, i.e., the smooth part can be adapted such that, additionally, the symmetry and the positivity condition are exactly satisfied.},
  language  = {en}
}