Probing the vacuum fluctuations in scalar ghost-free theories

Abstract

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 $\delta$-like potential, $V=\lambda \delta (x)$, 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 $⟨{\hat{\phi }}^2(x){⟩}_{\text{ren}}$ 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 non-locality $\ell$; for distances $x\gg \ell$ the non-local and local results agree, whereas for distances $x<\ell$ there is a difference.

17 pages, 7 figures, computer algebra code available at http://spintwo.net/static/2019.01.21/ , v2: matches the published version

References in corpus (2)

• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Counting ghosts in the "ghost-free" non-local gravity

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