The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone coordinate system for Lorentz boosts. Also in 1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as the uncertainty relations in the Lorentz-covariant world. It is possible to integrate these three papers to produce the harmonic oscillator wave function which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two coupled oscillators to derive the Lie algebra for the generators of the O(3,2) de Sitter group, which has ten generators. It is proven possible to contract this group to the inhomogeneous Lorentz group with ten generators, which constitute the fundamental symmetry of quantum mechanics in Einstein’s Lorentz-covariant world.

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整合狄拉克构建洛伦兹协变量子力学的努力

Paul AM Dirac 的毕生努力是在洛伦兹协变世界中构建局部量子系统。1927 年，他指出时间-能量的不确定性应该包含在洛伦兹协变图中。1945 年，他尝试使用定位在空间和时间变量中的可归一化高斯函数来构造洛伦兹群的表示。1949 年，他引入了他的瞬时形式来排除类似时间的振荡。他还介绍了洛伦兹增强的光锥坐标系。同样在1949年，他指出非齐次洛伦兹群的李代数可以作为洛伦兹协变世界中的不确定关系。可以综合这三篇论文来产生可以进行洛伦兹变换的谐振子波函数。此外，狄拉克在 1963 年，考虑两个耦合振荡器来推导出 O(3,2) de Sitter 群的发生器的李代数，该群有 10 个发生器。证明可以将该群收缩为具有十个发生器的非齐次洛伦兹群，这构成了爱因斯坦洛伦兹协变世界中量子力学的基本对称性。