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Non-relativistic fermion–fermion scattering in higher derivative gravity

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Abstract

In this note, the scattering of two identical fermions in theories where fermionic fields are minimally coupled to higher derivative gravity was examined. In particular, the extension of general relativity with \(R^2\) corrections or non-local terms was considered. The action of fermions around the flat space background was expanded, and two fermions–one graviton vertex was obtained. Then, the non-relativistic limit due to scattering amplitude was calculated and that leads to obtaining the potential of two fermion–fermion interaction which would be the usual Newtonian potential corrected with a Yukawa-like term. Finally , we briefly discuss the astronomical effects of such Yukawa-like potential by computing the gravitational pressure of a spherical star and use it for a white dwarf to obtain quantum corrections of Chandrasekhar radius.

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Acknowledgements

Mohammad A. Ganjali would like to thank Dr. Farzan Momeni for useful discussion about white dwarf and Chandrasekhar limit. Mohammad A. Ganjali would also like to thank the Kharazmi University for supporting the paper with grant.

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Authors and Affiliations

  1. Department of Physics, Kharazmi University, P. O. Box 31979-37551, Tehran, Iran

    Mohammad A. Ganjali & Vahid Amirkhani

  2. Department of Physics and Astronomy, Ohio University, 251B Clippinger Labs, Athens, OH, 45701, USA

    Ahmad ShamlouMehr

Authors
  1. Mohammad A. Ganjali
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  2. Vahid Amirkhani
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  3. Ahmad ShamlouMehr
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Correspondence to Mohammad A. Ganjali.

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Ganjali, M.A., Amirkhani, V. & ShamlouMehr, A. Non-relativistic fermion–fermion scattering in higher derivative gravity. Indian J Phys 94, 541–545 (2020). https://doi.org/10.1007/s12648-019-01469-9

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  • DOI: https://doi.org/10.1007/s12648-019-01469-9

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