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Second order Langevin equation and definition of quantum gravity by stochastic quantisation
Nuclear Physics B ( IF 2.8 ) Pub Date : 2020-06-09 , DOI: 10.1016/j.nuclphysb.2020.115090
Laurent Baulieu , Siye Wu

Euclidean quantum gravity might be defined by stochastic quantisation that is governed by a higher order Langevin equation rather than a first order stochastic equation. In a transitory phase where the Lorentz time cannot be defined, the parameter that orders the evolution of quantum gravity phenomena is the stochastic time. This changes the definition of causality in the period of primordial cosmology. The prediction of stochastically quantised gravity is that there will a transition from an oscillating quantum phase to a semi-classical one, when the Lorentz time emerges. The end of the transition, as it can be observed from now and described by inflation models, is a diluted Universe, following the inflation phenomenological evolution. It is filled at the beginning with scattered classical primordial black holes. The smallest ones will quickly decay in matter, with a standard quantum field theory evolution till our period. The stable heavier black holes will remain, forming a good fraction of the dark matter and the large black holes observed in the galaxies. In a theoretically related way, this framework suggests the possibility of a gravitational parton content for “point-like” particles, in the same five dimensional quantum field theory context as in the primordial cosmology, with a (+) signature for the 5d metrics. The very precise and explicit result expressed in this paper is actually far more modest than its motivation. We compute explicitly the meaning of a second order Langevin equation in zero dimensions and define precisely what is second order stochastic quantisation in a soluble case.



中文翻译:

二阶Langevin方程和量子引力的随机量化定义。

欧几里德量子引力可以通过由高阶Langevin方程而非一阶随机方程支配的随机量化来定义。在不能定义洛伦兹时间的过渡阶段,命令量子引力现象发展的参数是随机时间。这改变了原始宇宙学时期因果关系的定义。随机量化引力的预测是,当洛伦兹时间出现时,将从振荡量子相过渡到半经典相。从现在开始可以观察到并由通货膨胀模型描述的过渡的终点是遵循通货膨胀现象学演变的稀释宇宙。它在开始时充满了分散的古典原始黑洞。最小的物质将随着标准量子场论的发展而迅速衰变,直至我们的时期。较稳定的较重黑洞将保留下来,形成了很大比例的暗物质和在银河系中观测到的大黑洞。以一种理论上相关的方式,该框架暗示了在与原始宇宙学相同的五维量子场理论背景下,“点状”粒子的重力parton含量的可能性。+----5d指标的签名。本文中表达的非常精确和明确的结果实际上远比其动机适度。我们明确地计算零维二阶Langevin方程的含义,并精确定义什么是可溶情况下的二阶随机量化。

更新日期:2020-06-29
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