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.

arXiv comment17 pages, 7 figures, computer algebra code available at http://spintwo.net/static/2019.01.21/ , v2: matches the published version

References in corpus (17)

• Towards singularity and ghost free theories of gravity
• Super-renormalizable Quantum Gravity
• The Casimir effect: Recent controversies and progress
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Generalized ghost-free quadratic curvature gravity
• Classical properties of non-local, ghost- and singularity-free gravity
• Counting ghosts in the "ghost-free" non-local gravity
• The gravitational field of static p-branes in linearized ghost-free gravity
• Quantum vacuum energies and Casimir forces between partially transparent $\delta$-function plates
• Nonlocal theories of gravity: the flat space propagator
• Schwarzschild $1/r$-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity
• Transmutation of nonlocal scale in infinite derivative field theories
• Non-local gravity in D-dimensions: Propagator, entropy and bouncing Cosmology
• Radiation from an emitter in the ghost free scalar theory
• Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?
• Quantum scattering on a delta potential in ghost-free theory
• On memory effect in modified gravity theories

Cited by in corpus (13)

• Generalized ghost-free propagators in nonlocal field theories
• Ultrarelativistic spinning objects in non-local ghost-free gravity
• Non-unitarity of Minkowskian non-local quantum field theories
• Ghost-free modification of the Polyakov action and Hawking radiation
• On the contour prescriptions in string-inspired nonlocal field theories
• Unattainability of the Trans-Planckian regime in Nonlocal Quantum Gravity
• Retarded field of a uniformly accelerated source in non-local scalar field theory
• Form factors, spectral and Källén-Lehmann representation in nonlocal quantum gravity
• Asymptotic nonlocality
• Doubly special relativity as a non-local quantum field theory
• Topological defects in nonlocal field theories
• What happens to topological invariants (and black holes) in singularity-free theories?
• Resonant particle creation by a time-dependent potential in a nonlocal theory