论文标题
关于三个玻色子的正规化哈密顿官的一些评论
Some Remarks on the Regularized Hamiltonian for Three Bosons with Contact Interactions
论文作者
论文摘要
我们讨论了模型哈密顿量的某些特性，以在三个维度上通过零距离力相互作用的三个玻色子系统。为了避免众所周知的不稳定性现象，我们考虑了这种哈密顿量的所谓的Minlos-faddeev正则化，启发式上与引入三体排斥相对应。我们回顾了最近获得的有关结果的主要结果。特别是，从合适的二次表格$ q $开始，可以构建自偶会并从汉密尔顿$ \ mathcal h $界定，只要三体力的强度$γ$大于阈值参数$γ_c$。此外，每当$γ>γ'_c$时，我们给出了上述结果的替代性和简单证明，$γ'_c$严格大于$γ_c$。最后，我们表明阈值$γ_c$是最佳的，因为如果$γ<γ_c$，二次形式$ q $是无限的。
We discuss some properties of a model Hamiltonian for a system of three bosons interacting via zero-range forces in three dimensions. In order to avoid the well known instability phenomenon, we consider the so-called Minlos-Faddeev regularization of such Hamiltonian, heuristically corresponding to the introduction of a three-body repulsion. We review the main concerning results recently obtained. In particular, starting from a suitable quadratic form $Q$, the self-adjoint and bounded from below Hamiltonian $\mathcal H$ can be constructed provided that the strength $γ$ of the three-body force is larger than a threshold parameter $γ_c$. Moreover, we give an alternative and much simpler proof of the above result whenever $γ> γ'_c$, with $γ'_c$ strictly larger than $γ_c$. Finally, we show that the threshold value $γ_c$ is optimal, in the sense that the quadratic form $Q$ is unbounded from below if $γ<γ_c$.
