Abstract
The mathematics of coherent states is essentially a translation of oscillator quantum mechanics to the paraxial model of optics, and is based on the Heisenberg-Weyl algebra and group. On the other hand, “4a” optics is based on the three-dimensional Euclidean algebra and corresponding group. We show here that a global map between the two may be established. It is, in fact, third-order Seidel-Lie coma. Spherical and circular-comatic aberrations are a proper subgroup of the group of all canonical transformations of phase space, that can be subject to unique quantization and wavization.
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Man'ko, V.I., Wolf, K.B. (1989). The map between Heisenberg-Weyl and Euclidean optics is comatic. In: Wolf, K.B. (eds) Lie Methods in Optics II. Lecture Notes in Physics, vol 352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0012748
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DOI: https://doi.org/10.1007/BFb0012748
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