洛伦兹谐波、压缩谐波及其物理应用
Lorentz Harmonics, Squeeze Harmonics, and their Physical Applications
摘要：
在物理学的对称性中，旋转对称性是我们最熟悉的。众所周知，当世界旋转时，球谐函数是有用的。压缩变换在物理学中也变得越来越突出，特别是在光学科学和高能物理学中。从狄拉克的光锥坐标系可以看出，洛伦兹增强是压缩变换。因此，压缩变换是爱因斯坦的洛伦兹协变世界中的基本变换之一。可以定义一个洛伦兹坐标系的标准正交函数的完整集合。它表明，相同的设置可以用于其他洛伦兹框架。变换性质进行了讨论。物理应用在光学和高能物理中进行了讨论。结果表明，洛伦兹谐波为光的压缩态提供了数学基础。它还表明，同一套谐波可以用于理解洛伦兹增强强子在高能物理。这样，就有可能利用物理学的一个分支和另一个分支所共有的数学基础，把物理学从它们之间传递到另一个分支。
英文摘要：
Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac's light-cone coordinate system, Lorentz boosts are squeeze transformations. Thus the squeeze transformation is one of the fundamental transformations in Einstein's Lorentz-covariant world. It is possible to define a complete set of orthonormal functions defined for one Lorentz frame. It is shown that the same set can be used for other Lorentz frames. Transformation properties are discussed. Physical applications are discussed in both optics and high-energy physics. It is shown that the Lorentz harmonics provide the mathematical basis for squeezed states of light. It is shown also that the same set of harmonics can be used for understanding Lorentz-boosted hadrons in high-energy physics. It is thus possible to transmit physics from one branch of physics to the other branch using the mathematical basis common to them.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
