2019/01/31 by Jens Boos, Valeri P. Frolov, Andrei Zelnikov · 21 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometry #Lambda #Mathematical physics #Mathematics #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum entanglement #Quantum field theory #Quantum fluctuation #Quantum mechanics #Quantum nonlocality #Scalar (mathematics) #Scalar field #Vacuum expectation value #Vacuum polarization #hep-th
paper · pdf · doi:10.1103/physrevd.99.076014
published in Physical review. D/Physical review. D. 99(7) (American Physical Society) · 17 pages, 7 figures, computer algebra code available at http://spintwo.net/static/2019.01.21/ , v2: matches the published version
openalex publication_date 2019/04/26 · arxiv created 2019/04/29 · arxiv updated 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss the response of vacuum fluctuations to a static potential in the context of massive, ghost-free infinite-derivative scalar field theories in two dimensions. For the special case of a \ensuremathδ-like potential, V=\ensuremathλ\ensuremathδ(x), the problem is exactly solvable and we calculate the corresponding Hadamard function for this quantum field. Using this exact result we determine the renormalized value of the vacuum polarization ⟨\stackrel^\ensuremathφ2(x)⟩ren as a function of the distance x from the position of the potential. This expression depends on the amplitude of the potential as well as the scale of nonlocality \ensuremathℓ; for distances x\ensuremath≫\ensuremathℓ the nonlocal and local results agree, whereas for distances x<\ensuremathℓ there is a difference.