Smearing out contact terms in ghost-free infinite derivative quantum gravity

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Abstract
In the context of ghost-free infinite derivative gravity, we consider the single graviton exchange between two spinless particles, a spinless particle and a photon, or between a spinless particle and a spin-1/2 particle. To this end, we compute the gravitational potential for the three aforementioned cases and derive the O ( G ℏ 2 ) correction that arises at the linearised level. In the local theory, it is well-known that such a correction appears in the form of a Dirac delta function. Here, we show that this correction is smeared out for the nonlocal theory and, in contrast to the local theory, takes on non-zero values for a non-zero separation between the two particles. In the case of the single graviton exchange between a spinless particle and a spin-1/2 particle, we also compute the O ( G ℏ ) correction that arises in the non-static case within the non-relativistic approximation and show that it is finite in the nonlocal theory.
Funding Information
  • MCINU, Spain (BG20/00236 action)
  • CSIC (COOPB23096)
  • University of Groningen
  • National Research Foundation of South Africa (CSUR23042798041)
  • Universityof CapeTown
  • MCIN/AEI (PID2021-122938NB-I00)

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