AI 中文总结
研究利用三维光前量子力学构建相对论系统内部结构的洛伦兹不变波函数，以米勒 - 布罗茨基变量\(\tilde{z}\)为基础，通过相对论性谐振子势为例进行分析，探索相关条件，为原子核光前波函数提供基础。
AI 中文摘要
三维光前量子力学可用于构建相对论系统内部结构的洛伦兹不变波函数。与动量分数\(x\)正则共轭的米勒 - 布罗茨基变量\(\tilde{z}\)能对纵向自由度进行空间描述。本文展示了如何将\(\tilde{z}\)构建为算符并证明其洛伦兹不变性。以李、马里斯、赵和瓦里提出的相对论性谐振子势为例，该势可利用\(\tilde{z}\)构建且能找到封闭形式的解析解。系统探索了重现非相对论谐振子解的条件以及相对论修正显著的条件。谐振子态常用于核多体计算，当前工作可为提供原子核的光前波函数奠定基础。
英文摘要
Light front quantum mechanics in three dimensions can be used to construct boost-invariant wave functions for the internal structure of relativistic systems. The Miller-Brodsky variable $\tilde{z}$ -- which is canonically conjugate to the momentum fraction $x$ -- allows a spatial description of the longitudinal degree of freedom. We show how $\tilde{z}$ can be constructed as an operator and prove its boost invariance. A relativistic harmonic oscillator potential from Li, Maris, Zhao and Vary [Phys Lett B 758 (2016) 118] is used as an example of a two-body interaction that can be constructed using $\tilde{z}$ and for which closed-form analytic solutions can be found. We systematically explore the conditions in which the non-relativistic harmonic oscillator solutions are reproduced and the conditions in which relativistic corrections are significant. Harmonic oscillator states are commonly used as a basis for nuclear many-body calculations. The present effort may provide a basis for providing light-front wave functions of nuclei.
Comments19 pages, 2 figures
