What is it about?
An entirely new approach to canonical quantum gravity is presented. By writing the Ansatz corresponding to a Euclidean-signature HJE solution, the Bianchi IX Wheeler–DeWitt equation (or the Einstein–Schrödinger equation) is solved globally for the first time, with order-by-order transport equations that can be integrated along the flow of the Euclidean-signature HJE solution to find all the quantum correction terms to any order. Excitingly, we arrive at an infinite spectrum of discrete excited states for the Bianchi IX system, which postulated to exist by Misner some forty years ago, but now calculated in their explicit forms for the first time.
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Why is it important?
While the analysis in this paper is limited to spatially homogeneous cosmological models, we anticipate that the techniques used here should eventually be much more generally applicable, and thus represent a significant advance in the Wheeler–DeWitt approach to quantum gravity.
Perspectives
I set out to answer the question: “does the quantum mechanical principle of ‘confinement leading to quantization’ apply to our whole universe as well?”, and this paper formed a certain closure, strongly suggesting the affirmative. I hope that this research paves the way forward for others to build even more sophisticated models of the early universe and ultimately help answer the question of Dark Energy.
Dr Joseph Hongchul Bae
Read the Original
This page is a summary of: Mixmaster revisited: wormhole solutions to the Bianchi IX Wheeler–DeWitt equation using the Euclidean-signature semi-classical method, Classical and Quantum Gravity, March 2015, Institute of Physics Publishing,
DOI: 10.1088/0264-9381/32/7/075006.
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