High Energy Physics - Theory
[Submitted on 9 May 2018 (v1), last revised 28 May 2019 (this version, v3)]
Title:Ghost-free infinite derivative quantum field theory
View PDFAbstract:In this paper we will study Lorentz-invariant, infinite derivative quantum field theories, where infinite derivatives give rise to non-local interactions at the energy scale $M_s$, beyond the Standard Model. We will study a specific class, where there are no it new dynamical degrees of freedom other than the original ones of the corresponding local theory. We will show that the Green functions are modified by a non-local extra term that is responsible for acausal effects, which are confined in the region of non-locality, i.e. $M_s^{-1}.$ The standard time-ordered structure of the causal Feynman propagator is not preserved and the non-local analog of the retarded Green function turns out to be non-vanishing for space-like separations. As a consequence the local commutativity is violated. Formulating such theories in the non-local region with Minkowski signature is not sensible, but they have Euclidean interpretation. We will show how such non-local construction ameliorates ultraviolet/short-distance singularities suffered typically in the local quantum field theory. We will show that non-locality and acausality are inherently off-shell in nature, and only quantum amplitudes are physically meaningful, so that all the perturbative quantum corrections have to be consistently taken into account.
Submission history
From: Luca Buoninfante [view email][v1] Wed, 9 May 2018 14:42:17 UTC (120 KB)
[v2] Sun, 7 Oct 2018 15:13:25 UTC (123 KB)
[v3] Tue, 28 May 2019 10:45:13 UTC (116 KB)
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