标题： 半相对论N玻色子系统的结合能 显示英文标题

标题： Binding energies of semirelativistic N-boson systems

摘要： 对于由半相对论哈密顿量形式的N玻色子系统，推导出了一般的解析能量界限 H=\sum _{i=1}^N \sqrt (p_i^2+m^2) + \sum _{1=i<j}^N V(r_{ij}), 其中V(r)是一个静态吸引势。 构造了一个平移不变模型哈密顿量H_c。 我们猜想<H> \ge <H_c>通常成立，并且我们证明了当N=3时，以及当m=0时N=4的情况。 该猜想对于谐波振荡器和非相对论大m极限情况也普遍有效。 这种表述允许简化为缩放的三体或四体问题，其谱底提供了能量下限。 详细研究了超相对论线性势的例子，并推导出了显式的上下界公式，并与早期的界限进行了比较。 显示英文摘要

摘要： General analytic energy bounds are derived for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N \sqrt(p_i^2+m^2) + \sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. A translation-invariant model Hamiltonian H_c is constructed. We conjecture that <H> \ge <H_c> generally, and we prove this for N=3, and for N=4 when m=0. The conjecture is also valid generally for the harmonic oscillator and in the nonrelativistic large-m limit. This formulation allows reductions to scaled 3- or 4-body problems, whose spectral bottoms provide energy lower bounds. The example of the ultrarelativistic linear potential is studied in detail and explicit upper- and lower-bound formulas are derived and compared with earlier bounds.