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Tales from the prehistory of Quantum Gravity
The European Physical Journal H ( IF 1 ) Pub Date : 2018-04-12 , DOI: 10.1140/epjh/e2018-80018-6
Giulio Peruzzi , Alessio Rocci

The main purpose of this paper is to analyse the earliest work of Léon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld tried to face this problem in 1927, analysing the role of his mentors: Oskar Klein, Louis de Broglie and Théophile De Donder. Rosenfeld asked himself how quantum mechanics should concretely modify general relativity. In the context of a five-dimensional theory, Rosenfeld tried to construct a unifying framework for the gravitational and electromagnetic interaction and wave mechanics. Using a sort of “general relativistic quantum mechanics” Rosenfeld introduced a wave equation on a curved background. He investigated the metric created by what he called ‘quantum phenomena’, represented by wave functions. Rosenfeld integrated Einstein equations in the weak field limit, with wave functions as source of the gravitational field. The author performed a sort of semi-classical approximation obtaining at the first order the Reissner-Nordström metric. We analyse how Rosenfeld’s work is part of the history of Quantum Mechanics, because in his investigation Rosenfeld was guided by Bohr’s correspondence principle. Finally we briefly discuss how his contribution is connected with the task of finding out which metric can be generated by a quantum field, a problem that quantum field theory on curved backgrounds will start to address 35 years later.

中文翻译:

量子引力史前的故事

本文的主要目的是分析从事量子引力研究的先驱之一莱昂·罗森菲尔德(LéonRosenfeld)的工作,该理论将量子理论与广义相对论结合起来。我们通过分析其导师的角色:奥斯卡·克莱因(Oskar Klein),路易·德布罗意(Louis de Broglie)和泰奥菲尔·德·唐德(ThéophileDe Donder),来描述罗森菲尔德在1927年如何以及为什么试图面对这个问题。罗森菲尔德问自己,量子力学应该如何具体修改广义相对论。在五维理论的背景下,罗森菲尔德试图为重力和电磁相互作用以及波力学构建统一的框架。Rosenfeld使用一种“广义相对论量子力学”在弯曲的背景上引入了波动方程。他研究了由他称为“量子现象”(由波函数表示)创建的度量。Rosenfeld在弱场极限中集成了爱因斯坦方程,其中波函数是引力场的来源。作者进行了一类半经典的近似,以一阶获得Reissner-Nordström度量。我们分析罗森菲尔德的工作是量子力学历史的一部分,因为罗森菲尔德的研究遵循玻尔的对应原理。
更新日期:2018-04-12
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