FQ‑Dirac封装模型下电子作为束缚态的数值证据
Year: 2026
Type: preprint
Abstract: English Abstract Within the framework of the FQ fractal nesting hypothesis, this study treats the electron as a Dirac fermion bound state encapsulated and constrained by a scalar field \phi(r) \propto 1/r^2. Adopting the shooting numerical solution scheme for the radial Dirac equation, we establish rigorous tail decay criteria for wave functions to eliminate a large number of mathematically valid but physically spurious solutions. A bound-state energy level highly consistent with the electron rest energy of 0.511 MeV is found in the discrete parameter space. The optimal eigenenergy is E = 0.51089 MeV, with a relative deviation of −0.021%, which falls within the range of numerical calculation error. The numerical results support the physical picture that electrons possess an internal encapsulated structure, and electron mass originates from the bound-state energy spectrum of such structure. 中文摘要 本研究在FQ分形嵌套假说框架之下,将电子视作被标量场 \phi(r) \propto 1/r^2 封装约束的狄拉克费米子束缚态。采用径向狄拉克方程打靶(shooting)数值求解方案,建立严格的波函数尾部衰减判据,剔除大量数学形式成立但物理无效的赝解。在离散参数空间中寻得与电子静能 0.511 MeV 高度吻合的束缚态能级,最优解本征能量 E = 0.51089 MeV,相对偏差 -0.021%,处于数值计算误差范围。数值结果支持“电子内部存在封装结构,质量来源于束缚态能谱”这一物理图像。
Author: Bian, Zhenfeng
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204638962