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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 Schr\"odinger equation distinguishing classical and quantum contributions from the wave function field. 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 binding with a Bohr radius $$a$$ as being $$\Lambda=3/a^2$$. This is the same relation as for the de Sitter cosmological horizon.

### Author and article information

###### Journal
1312.1316

General relativity & Quantum cosmology