发表机构
Nagoya Aoi University（名古屋葵大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一维狄拉克系统中三体完整相位作为族三重化与质量层级玩具模型，通过C3不变质量算符产生轻分支并保留环路记忆，为相关唯象提供概念验证。
AI 中文摘要
我们研究一维空间相对论性狄拉克系统中真实三体完整相位的唯象后果。在移除质心坐标后，三重重合点刺穿二维相对构型空间，允许非平凡的$U(1)$绕数相位，而成对的Sakamoto--Munakata--Ino接触相互作用在该点周围给出平凡的净匹配。在固定内禀宇称下，六个粒子排序扇区约化为三维循环空间。一个厄米$C_3$不变有效质量算符允许Peierls型实现，其中围绕三个链路的规范不变相位等于三体完整相位$\theta_3$。其本征值为$$ M^{[k]}=M_0+2\Delta\cos\\!\left(\frac{\theta_3+2\pi k}{3}\right), \qquad k=0,1,2. $$ 该完整相位解除共轭通道简并，并可通过公共质量与完整相位诱导位移之间的抵消产生参数化轻分支。我们进一步允许循环对称性破缺，并考虑一般厄米三态质量矩阵。通过Schur补精确消除两个重态，得到包含重定相不变环路乘积$\mathrm{Re}(t_{12}t_{23}t_{31})\propto\cos\theta_3$的低能修正。因此，即使仅一个分支在运动学上可及，其有效质量仍可保留完整三态环路的有限记忆。互补不变量$\mathrm{Im}(t_{12}t_{23}t_{31})\propto\sin\theta_3$对相位敏感，但单独并不蕴含CP破坏。该构造提供了族三重化、质量层级和红外记忆的低维唯象概念验证，而非标准模型费米子代的微观理论。
英文摘要
We investigate the phenomenological consequences of a genuine three-body holonomy in a relativistic Dirac system in one spatial dimension. After removing the center-of-mass coordinate, the triple-coincidence point punctures the two-dimensional relative configuration space and permits a nontrivial $U(1)$ winding phase, whereas the pairwise Sakamoto--Munakata--Ino contact interactions give trivial net matching around this point. At fixed intrinsic parity, the six particle-ordering sectors reduce to a three-dimensional cyclic space. A Hermitian $C_3$-invariant effective mass operator admits a Peierls-type realization in which the gauge-invariant phase around the three links equals the three-body holonomy $θ_3$. Its eigenvalues are $$ M^{[k]}=M_0+2Δ\cos\!\left(\frac{θ_3+2πk}{3}\right), \qquad k=0,1,2. $$ The holonomy lifts the conjugate-channel degeneracy and can generate a parametrically light branch through cancellation between the common mass and the holonomy-induced shift. We further allow cyclic-symmetry breaking and consider a general Hermitian three-state mass matrix. Exact elimination of two heavy states by the Schur complement yields a low-energy correction containing the rephasing-invariant loop product $\mathrm{Re}(t_{12}t_{23}t_{31})\propto\cosθ_3$. Thus, even when only one branch is kinematically accessible, its effective mass can retain finite memory of the complete three-state loop. The complementary invariant $\mathrm{Im}(t_{12}t_{23}t_{31})\propto\sinθ_3$ is phase sensitive but does not alone imply CP violation. The construction provides a low-dimensional phenomenological proof of concept for family-like triplication, mass hierarchy, and infrared memory, rather than a microscopic theory of Standard Model fermion generations.
Comments10 pages, 4 figures
