AI 中文总结
该研究构建狄拉克系统和电子的因果逻辑协变表示，基于守恒流和定位过程，通过多项式衰减估计验证条件。建立结构性质，扩展结果到一般区域，分析高 boost 极限，还讨论了电子正电子分解及测量诱导的状态变换。
AI 中文摘要
我们基于守恒的狄拉克概率流和对非时间顺序区域的一般电流到定位过程，构建了狄拉克系统和电子的因果逻辑协变表示。通过非平稳相位论证得出的多项式衰减估计，验证了为完整狄拉克系统定义协变非时间顺序定位所需的条件。将此定位扩展到完整时空区域得到相应的因果逻辑表示；限制在正能量不变子空间给出电子的类似构造。我们建立了几个结构性质。在欧几里得空间上，狄拉克定位与规范投影值定位一致，而其位置算子与牛顿 - 维格纳算子相差一个明确确定的有界自伴修正。完整狄拉克非时间顺序定位是投影值的，并通过正交性表示非时间顺序分离，从而满足微观因果性。压缩到电子子空间后，它变为正算子值同时保持因果性。我们进一步将已知结果从空间扩展到一般非时间顺序区域，证明分离和范数为一的标准，并分析高 boost 极限，在精确概率意义上获得洛伦兹收缩。最后，我们讨论电子 - 正电子分解和位置测量引起的状态变换，表明测量引起的正电子产生是普遍的且与特定测量设备无关。
英文摘要
We construct a covariant representation of the causal logic for the Dirac system and the electron, based on the conserved Dirac probability current and a general current-to-localization procedure for achronal regions. A polynomial decay estimate, derived by a non-stationary phase argument, verifies the conditions required to define covariant achronal localization for the full Dirac system. Extending this localization to complete spacetime regions yields the corresponding causal-logic representation; restriction to the positive-energy invariant subspace gives the analogous construction for the electron. We establish several structural properties. On Euclidean space, Dirac localization agrees with canonical projection-valued localization, while its position operator differs from the Newton--Wigner operator by an explicitly determined bounded self-adjoint correction. Full Dirac achronal localization is projection valued and represents achronal separateness by orthogonality, thus satisfying microscopic causality. After compression to the electron subspace, it becomes positive-operator valued while preserving causality. We further extend known results from spatial to general achronal regions, prove separation and norm-one criteria, and analyze the high-boost limit, obtaining Lorentz contraction in a precise probabilistic sense. Finally, we discuss the electron--positron decomposition and the state transformation induced by position measurements, showing that measurement-induced positron production is universal and independent of the specific measuring device.
Comments46 pages, one figure
