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).

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） ）。