论文标题
部分可观测时空混沌系统的无模型预测
Random fields, large deviations and triviality in quantum field theory. Part II
论文作者
论文摘要
在这项工作的第一部分中开发的方法部分基于大偏差，导致相互作用的标量场不存在，因为有限体积和尺寸的正规化场的强限制$ d \ geq 4 $。第二部分涉及弱极限问题，对于$φ^{4} $的特定情况，根据第一部分中确定的3例情况，在两种情况下，这表明弱极限是微不足道的，因为限制字段相同为无效。对于第三种情况，获得了部分结果。这些结果与导致高斯自由场的已经知道的微不足道结果不相容。作为这项研究的产物，建立了对量子标量字段最小动作原理的严格表述，以及一组动态场方程，这些方程提供了Schwinger函数的明确表达。
The approach developed in the first part of this work, partly based on large deviations, led to the non-existence of interacting scalar fields as strong limits of regularized fields in finite volume and dimensions $d\geq 4$. This second part deals with the weak limit problem, for the particular case of $φ^{4}$, according to the 3 cases identified in Part I. In two of theses cases, it is shown that the weak limit is trivial in the sense that the limiting field is identically null. Partial results are obtained for the third case. These results are not incompatible with the already known triviality results that led to a Gaussian free field. As a by product of this study, a rigorous formulation of the principle of the least action for quantum scalar fields is established, together with a set of dynamic field equations that provide explicit expressions of the Schwinger functions.
