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arXiv · 1901.07096

Probing the vacuum fluctuations in scalar ghost-free theories

Jens Boos·Valeri P. Frolov·Andrei Zelnikov
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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 $\langle \hat{\varphi}^2(x)\rangle_\text{ren}$ 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.

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Jens Boos, Valeri P. Frolov, Andrei Zelnikov. 2019-01-21. Probing the vacuum fluctuations in scalar ghost-free theories. https://doi.org/10.1103/physrevd.99.076014

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