Sanders K (2024)
Publication Type: Journal article
Publication year: 2024
Book Volume: 405
Article Number: 132
Journal Issue: 5
DOI: 10.1007/s00220-024-05017-3
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 tμ we can find constants c,C>0 such that ω(ϕ(f)∗ϕ(f))≤C(ω(Tμνren(tμtνF2))+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(Tμνren(tμtνF2))+c), where F≡1 near x.
APA:
Sanders, K. (2024). Stress Tensor Bounds on Quantum Fields. Communications in Mathematical Physics, 405(5). https://doi.org/10.1007/s00220-024-05017-3
MLA:
Sanders, Ko. "Stress Tensor Bounds on Quantum Fields." Communications in Mathematical Physics 405.5 (2024).
BibTeX: Download