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The Dispersion of Newton's Constant: A Transfer Matrix Formulation of Quantum Gravity

J. Greensite
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Abstract

A transfer matrix formalism applicable to certain reparametrization invariant theories, including quantum gravity, is proposed. In this formulation it is found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt equation, but each with a different value of the Planck mass; the value $m_{Planck}^4$ turns out to be proportional to the eigenvalue of the evolution operator. As a consequence, the fact that the Universe is non-stationary implies that it is not in an eigenstate of Newton's constant.

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J. Greensite. 1993-09-13. The Dispersion of Newton's Constant: A Transfer Matrix Formulation of Quantum Gravity. https://doi.org/10.1103/physrevd.49.930

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