Lorentz Harmonics, Squeeze Harmonics, and their Physical Applications

TL;DR

This paper introduces Lorentz and squeeze harmonics as a unified mathematical framework with applications in optics and high-energy physics, demonstrating their role in describing squeezed states of light and boosted hadrons.

Contribution

It presents a complete set of orthonormal functions applicable across Lorentz frames, linking optical and high-energy physics through a common mathematical basis.

Findings

Lorentz harmonics underpin squeezed states of light.

The same harmonics describe Lorentz-boosted hadrons.

Unified mathematical framework for different physics domains.

Abstract

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.