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Stress Tensor Bounds on Quantum Fields

Sanders, Ko

Communications in mathematical physics, 2024-05, Vol.405 (5), Article 132 [Periódico revisado por pares]

Berlin/Heidelberg: Springer Berlin Heidelberg

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  • Título:
    Stress Tensor Bounds on Quantum Fields
  • Autor: Sanders, Ko
  • Assuntos: Classical and Quantum Gravitation ; Complex Systems ; Fields (mathematics) ; Hamiltonian functions ; Manifolds (mathematics) ; Mathematical and Computational Physics ; Mathematical Physics ; Minkowski space ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Polynomials ; Quantum Physics ; Relativity Theory ; Scalars ; Tensors ; Theoretical
  • É parte de: Communications in mathematical physics, 2024-05, Vol.405 (5), Article 132
  • Descrição: 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 ∈ C 0 ∞ ( 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 ( T μ ν 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 ( T μ ν ren ( t μ t ν F 2 ) ) + c ) , where F ≡ 1 near x .
  • Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
  • Idioma: Inglês
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