发表机构
İzmir Institute of Technology; Boğaziçi University（伊兹密尔理工大学; 博阿齐奇大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究一维半相对论玻色子接触相互作用的重整化，通过扩大福克空间和舒尔补方法消除对数紫外发散，证明非相对论极限回到利布-林尼格模型，并在平均场近似下预测束缚标度指数增长。
AI 中文摘要
我们研究具有半相对论自旋零-萨耳彼特色散关系和吸引性两体接触相互作用的一维无自旋玻色子。由于色散在大动量下变为线性，接触相互作用在幂次计数下是边缘的，并产生对数紫外发散。我们利用扩大的福克空间和预解式的舒尔补表示构建了重整化的多体理论，用物理的零总动量两体束缚态能量替代裸耦合常数。由此得到的与截断无关的预解式在每个固定粒子数扇区中定义了一个自伴哈密顿量。我们明确处理了两体问题，并在范数-预解式意义上证明了非相对论极限重现吸引性的利布-林尼格哈密顿量。我们还直接在重整化理论内提出了一个平均场近似。在无质量和大粒子数深束缚态区域，它预测了一个指数增长的束缚标度，其指数由一维变分问题决定。
英文摘要
We study one-dimensional spinless bosons with semirelativistic spinless-Salpeter dispersion and attractive pairwise contact interactions. Because the dispersion becomes linear at large momentum, the contact interaction is marginal by power counting and produces a logarithmic ultraviolet divergence. We construct the renormalized many-body theory using an enlarged Fock space and a Schur-complement representation of the resolvent, eliminating the bare coupling in favor of the physical zero-total-momentum two-body bound-state energy. The resulting cutoff-independent resolvent defines a self-adjoint Hamiltonian in each fixed particle-number sector. We treat the two-body problem explicitly and show, in the norm-resolvent sense, that the nonrelativistic limit reproduces the attractive Lieb--Liniger Hamiltonian. We also formulate a mean-field approximation directly within the renormalized theory. In the massless and deeply bound large-particle-number regimes, it predicts an exponentially increasing binding scale whose exponent is determined by a one-dimensional variational problem.
Comments49 pages
