Summary
In order to solve the negative-energy crisis in canonical quantum gravity, we generalize the correspondence principle, including the gravitational constant in the four-momentum operator. A physically consistent concept of time and, consequently, a wave equation equivalent to the Schrödinger equation are then introduced. Implications of this framework in quantum cosmology and in the predictability problem of quantum gravity are also discussed.
Riassunto
Per risolvere la crisi di energia negativa nella gravità quantistica canonica si generalizza il principio di corrispondenza, includendo la costante gravitazionale nell’operatore quadrimpulso. Sono quindi introdotti un concetto coerente di tempo e, di conseguenza, un’equazione d’onda equivalente all’equazione di Schrödinger. Si discutono anche le implicazioni di questo modello nella cosmologia quantistica e nel problema di prevedibilità della gravità quantistica.
Резюме
Мы обобщаем принцип соответствия, включая гравитационную постоянную в оператор четырех-импульса. Затем вводятся физически согласованная концепция времени и, следовательно, волновое уравнение, эквивалентное уравнению Шредингера. Также обсуждаются применения этого подхода к квантовой космологии и к проблеме предсказуемости для квантовой гравитации.
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González-Díaz, P.F. Correspondence principle in general relativity. Nuov Cim B 102, 195–207 (1988). https://doi.org/10.1007/BF02726567
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DOI: https://doi.org/10.1007/BF02726567