Foundations of Physics ( IF 1.2 ) Pub Date : 2021-05-26 , DOI: 10.1007/s10701-021-00470-9 Giacomo Gradenigo , Roberto Livi
We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021).
中文翻译:
辛量化I:相对论场论中量子涨落的动力学
我们在这里提出一种新的辛量化方案,其中标量场理论的量子涨落基于两个主要假设:相对论不变性和具有相同作用值的场构型的等概率。在这种方法中,相对于相对论坐标时间,虚拟量化的虚拟时间变成了真正的附加时间变量。这个内在的时间与动作空间中的辛进化有关,这不仅使人们能够研究理论的渐近(即平衡)性质,而且可以研究其非平衡瞬态演化。在本文中,这是两个系列中的第一个,我们介绍了一种形式主义,该形式主义将在其相对论中用于广义相对论(Gradenigo,辛量化II:时空量子涨落的动力学和宇宙常数,2021年) )。