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A new approach to quantum gravity: a summary

Sarah B. M. Bell·John P. Cullerne·Bernard M. Diaz
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Abstract

Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully resulted in QED is applied to General Relativity the theory obtained is not renormalizable. We derive a different method of quantising classical electromagnetism which also results in QED. We call the method the versatile method. We then apply the versatile method to General Relativity, in particular the Einstein equation which equates a geometrical description derivable from the metric to the energy-momentum-stress tensor, or as we shall call it the matter tensor of the matter field. The method can be applied provided that there is always a reference frame, which may differ with location and time, where the matter tensor can be reduced to a mass density with the other elements zero. We call such matter tensors simple. This restriction means that the tensor can be put into one to one correspondence with the Dirac current. When the versatile method of quantising a classical theory is applied to General Relativity the theory that results is renormalizable. It is in fact isomorphic to QED, provided that the temporal and a spatial co-ordinate are exchanged.

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Sarah B. M. Bell, John P. Cullerne, Bernard M. Diaz. 2002-11-27. A new approach to quantum gravity: a summary. https://arxiv.org/abs/gr-qc/0011008

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