57639
2022
2022
eng
34
1
63
article
American Institute of Physics
Melville
1
2022-01-03
2022-01-03
--
Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes
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 Hörmander [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 Bär, Ginoux, and Pfäffle {Wave Equations on Lorentzian Manifolds and Quantization [European Mathematical Society (EMS), Zürich, 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.
Journal of mathematical physics
10.1063/5.0055753
0022-2488
1089-7658
outputup:dataSource:WoS:2022
013501
WOS:000739446000005
Lewandowski, M (corresponding author), Potsdam Univ, Inst Math, Karl Liebknecht Str 24-25, D-14476 Potsdam, Germany., max.lewandowski@outlook.com
Lewandowski, Max
2023-01-23T13:17:05+00:00
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Max Lewandowski
Mathematik
Physik
Institut für Mathematik
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