581 research outputs found
Resurgent Deformation Quantisation
We construct a version of the complex Heisenberg algebra based on the idea of
endless analytic continuation. In particular, we exhibit an integral formula
for the product of resurgent operators with algebraic singularities. This
algebra would be large enough to capture quantum effects that escape ordinary
formal deformation quantisation.Comment: 28 pages, v2: published versio
Quantum fields from global propagators on asymptotically Minkowski and extended de Sitter spacetimes
We consider the wave equation on asymptotically Minkowski spacetimes and the
Klein-Gordon equation on even asymptotically de Sitter spaces. In both cases we
show that the extreme difference of propagators (i.e. retarded propagator minus
advanced, or Feynman minus anti-Feynman), defined as Fredholm inverses, induces
a symplectic form on the space of solutions with wave front set confined to the
radial sets. Furthermore, we construct isomorphisms between the solution spaces
and symplectic spaces of asymptotic data. As an application of this result we
obtain distinguished Hadamard two-point functions from asymptotic data.
Ultimately, we prove that the corresponding Quantum Field Theory on
asymptotically de Sitter spacetimes induces canonically a QFT beyond the future
and past conformal boundary, i.e. on two even asymptotically hyperbolic spaces.
Specifically, we show this to be true both at the level of symplectic spaces of
solutions and at the level of Hadamard two-point functions.Comment: 53 p., 4 figures; introduction and App. A.2 expanded, minor
improvements; to appear in Ann. Henri Poincar\'
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