论文标题
在两个空间维度中，相对论纳尔逊模型的最小能量的Feynman-kac公式和渐近行为
Feynman-Kac formula and asymptotic behavior of the minimal energy for the relativistic Nelson model in two spatial dimensions
论文作者
论文摘要
我们考虑了两个空间维度的重新归一化的相对论纳尔逊模型，用于与大量标量量化辐射场相互作用时有限数量的无旋转相对论量子机械物质颗粒。我们为相应的半集团找到了一个Feynman-kac公式，并讨论了一些含义，例如千古和加权$ l^p $到$ l^q $边界，对于在适当的相对主义意义上可以分解的外部电位。此外，当忽略物质粒子的保利原理时，我们的分析需要最小能量的上限和下限。在翻译中不变的情况（无外部电势），这些边界可以计算出三种粒子数量到无穷大的三个方案中最小能量的主要渐近剂，而物质辐射相互作用的耦合常数为无穷大，而玻色子质量为零。
We consider the renormalized relativistic Nelson model in two spatial dimensions for a finite number of spinless, relativistic quantum mechanical matter particles in interaction with a massive scalar quantized radiation field. We find a Feynman-Kac formula for the corresponding semigroup and discuss some implications such as ergodicity and weighted $L^p$ to $L^q$ bounds, for external potentials that are Kato decomposable in the suitable relativistic sense. Furthermore, our analysis entails upper and lower bounds on the minimal energy for all values of the involved physical parameters when the Pauli principle for the matter particles is ignored. In the translation invariant case (no external potential) these bounds permit to compute the leading asymptotics of the minimal energy in the three regimes where the number of matter particles goes to infinity, the coupling constant for the matter-radiation interaction goes to infinity and the boson mass goes to zero.
