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Symmetry 2011, 3(1), 16-36; doi:10.3390/sym3010016
Review

Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications

1,*  and 2
Received: 6 January 2011; in revised form: 7 February 2011 / Accepted: 11 February 2011 / Published: 14 February 2011
(This article belongs to the Special Issue Quantum Symmetry)
Download PDF [251 KB, updated 15 February 2011; original version uploaded 14 February 2011]
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.
Keywords: Lorentz harmonics; relativistic quantum mechanics; squeeze transformation; Dirac’s efforts; hidden variables; Lorentz-covariant bound states; squeezed states of light Lorentz harmonics; relativistic quantum mechanics; squeeze transformation; Dirac’s efforts; hidden variables; Lorentz-covariant bound states; squeezed states of light
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Kim, Y.S.; Noz, M.E. Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications. Symmetry 2011, 3, 16-36.

AMA Style

Kim YS, Noz ME. Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications. Symmetry. 2011; 3(1):16-36.

Chicago/Turabian Style

Kim, Young S.; Noz, Marilyn E. 2011. "Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications." Symmetry 3, no. 1: 16-36.


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