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

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

1993-09-13

arxiv.org/abs/gr-qc/9309010v1

Phys.Rev. D49 (1994) 930-940

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, plain LaTeX, NBI-HE-93-54

Scientific paper

10.1103/PhysRevD.49.930

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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