标题： 辛量化与闵可夫斯基统计力学：在1+1格点上的模拟 显示英文标题

标题： Symplectic Quantization and Minkowskian Statistical Mechanics: simulations on a 1+1 lattice

摘要： 我们引入了辛量子化，这是一种新颖的功能性方法，用于量子场论，它允许直接在闵可夫斯基时空内对量子场涨落进行采样，这与传统的仅适用于欧几里得场论的重要性采样协议不同。这种重要性采样过程是通过一个由哈密顿类似方程生成的确定性动力学实现的，该方程相对于一个辅助时间参数$\tau$进行演化。在这个框架中，量子涨落的期望值是作为沿由$\tau$参数化的轨迹的动力学平均值来计算的。假设遍历性，这等价于采样一个微正则配分函数。然后，通过一个大-M计算，其中M是格点上的自由度数量，我们证明微正则关联函数等同于由闵可夫斯基规范理论产生的关联函数，其中量子场涨落由因子$\exp(S/\hbar )$加权，$S$是系统的原始相对论作用量。 显示英文摘要

摘要： We introduce symplectic quantization, a novel functional approach to quantum field theory which allows to sample quantum fields fluctuations directly in Minkowski space-time, at variance with the traditional importance sampling protocols, well defined only for Euclidean Field Theory. This importance sampling procedure is realized by means of a deterministic dynamics generated by Hamilton-like equations evolving with respect to an auxiliary time parameter $\tau$. In this framework, expectation values over quantum fluctuations are computed as dynamical averages along the trajectories parameterized by $\tau$. Assuming ergodicity, this is equivalent to sample a microcanonical partition function. Then, by means of a large-M calculation, where M is the number of degrees of freedom on the lattice, we show that the microcanonical correlation functions are equivalent to those generated by a Minkowskian canonical theory where quantum fields fluctuations are weighted by the factor $\exp(S/\hbar )$, with $S$ being the original relativistic action of the system.