This article delves into the application of Dimer images in addressing two-body problems within lattice quantum chromodynamics (LQCD), providing the finite volume energy spectrum of deuterons in the context of ${}^{3}S_1$-${}^{3}D_1$ coupled-channels. The author commences by introducing the Dimer-particle method and formulating the Lagrangian for the scattering of two fermions. Additionally, the author defines the relativistic high partial zeta-function in a moving reference system and outlines a method for its rapid convergence calculation. The article further scrutinizes zeta-function representations across various momentum shells and discusses issues related to symmetry breakdown in specific momentum configurations. In sum, this work presents innovative methods for incorporating spin and isospin indices into dimer models, thereby establishing closer relevance to LQCD and deuteron studies.

本文深入研究了二聚体图像在解决晶格量子色动力学 (LQCD) 中的双体问题中的应用，提供了氘核的有限体积能谱${}^{3}S_1$-${}^{3}D_1$耦合通道。作者首先介绍了二聚体粒子方法并制定了两个费米子散射的拉格朗日量。此外，作者定义了运动参考系中的相对论高偏zeta函数，并概述了其快速收敛计算的方法。本文进一步仔细研究了各种动量壳层的 zeta 函数表示，并讨论了与特定动量构型中对称性破坏相关的问题。总之，这项工作提出了将自旋和同位旋指数纳入二聚体模型的创新方法，从而与 LQCD 和氘核研究建立更紧密的相关性。