Foundations of Physics

, Volume 45, Issue 11, pp 1465–1482 | Cite as

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

  • T. S. Biró
  • P. Ván


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 \(\Lambda =3/a^2\).


Cosmological constant problem Madelung transformation  Gravonium Partial conformal symmetry Bohm–Takabayashi energy–momentum tensor 



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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Authors and Affiliations

  1. 1.Department of Theoretical PhysicsMTA Wigner Research Centre for PhysicsBudapestHungary

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