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@article{faucris.322809410,
abstract = {The singular behaviour of quantum fields in Minkowski space can often be bounded by polynomials of the Hamiltonian H. These so-called H-bounds and related techniques allow us to handle pointwise quantum fields and their operator product expansions in a mathematically rigorous way. A drawback of this approach, however, is that the Hamiltonian is a global rather than a local operator and, moreover, it is not defined in generic curved spacetimes. In order to overcome this drawback we investigate the possibility of replacing H by a component of the stress tensor, essentially an energy density, to obtain analogous bounds. For definiteness we consider a massive, minimally coupled free Hermitean scalar field. Using novel results on distributions of positive type we show that in any globally hyperbolic Lorentzian manifold M for any f,F∈C0^{∞}(M) with F≡1 on supp(f) and any timelike smooth vector field t^{μ} we can find constants c,C>0 such that ω(ϕ(f)^{∗}ϕ(f))≤C(ω(Tμν^{ren}(t^{μ}t^{ν}F^{2}))+c) for all (not necessarily quasi-free) Hadamard states ω. This is essentially a new type of quantum energy inequality that entails a stress tensor bound on the smeared quantum field. In 1+1 dimensions we also establish a bound on the pointwise quantum field, namely |ω(ϕ(x))|≤C(ω(Tμν^{ren}(t^{μ}t^{ν}F^{2}))+c), where F≡1 near x.},
author = {Sanders, Ko},
doi = {10.1007/s00220-024-05017-3},
faupublication = {yes},
journal = {Communications in Mathematical Physics},
note = {CRIS-Team Scopus Importer:2024-05-24},
peerreviewed = {Yes},
title = {{Stress} {Tensor} {Bounds} on {Quantum} {Fields}},
volume = {405},
year = {2024}
}