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Splitting the Source Term for the Einstein Equation to Classical and Quantum Parts

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Abstract

We consider the special and general relativistic extensions of the action principle behind the Schrödinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the classical Einstein equation we identify the conformal content of the above action and obtain classical gravitation for massive particles, but with a cosmological term representing off-mass-shell contribution to the energy–momentum tensor. In this scenario the—on the Planck scale surprisingly small—cosmological constant stems from quantum bound states (gravonium) having a Bohr radius a as being \(\Lambda =3/a^2\).

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Notes

  1. It is so in order to transform a traceless tensor to another traceless one by a conformal transformation.

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Acknowledgments

We thank Manfried Faber for detailed discussions. Antal Jakovác, András Patkós and Reinhard Alkofer contributed with inspiring remarks at the ACHT (Austrian-Croatian-Hungarian Triangle) Meeting in Retzhof, June 2013. We also thank to the referees for the constructive remarks. This work was supported by the Hungarian National Research Fund OTKA (K81161, K104260).

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  1. Department of Theoretical Physics, MTA Wigner Research Centre for Physics, Budapest, Hungary

    T. S. Biró & P. Ván

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Biró, T.S., Ván, P. Splitting the Source Term for the Einstein Equation to Classical and Quantum Parts. Found Phys 45, 1465–1482 (2015). https://doi.org/10.1007/s10701-015-9920-7

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