Abstract
This contribution to the Proceedings bears the same title as the chapter by this author published in Progress in Optics, and recovers the basic construction starting from the compact algebras so(3) or so(4) for 1- and 2-dimensional finite pixellated-screen optics and their contraction to the Euclidean algebras, in which the geometric and wave models find their realization determined by two symmetry subalgebras, but with questions that may prompt further research. Here we follow and question the path from pixellated-screen optics to three-dimensional geometric optics by contraction between Lie algebras and groups.
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References
N. M. Atakishiyev and K. B. Wolf, J. Opt. Soc. Am. A 14, 1467 (1997).
N. M. Atakishiyev, G. S. Pogosyan, and K. B. Wolf, Phys. Part. Nucl. Suppl. 3 36, 521 (2005).
N. M. Atakishiyev, G. S. Pogosyan, L. E. Vicent, and K. B. Wolf, J. Phys. A 34, 9381 (2001).
N. M. Atakishiyev, G. S. Pogosyan, L. E. Vicent, and K. B. Wolf, J. Phys. A 34, 9399–9415 (2001).
K. B. Wolf, Optical models and symmetries, in Progress in Optics, Ed. by T. D. Visser (Elsevier, 2017), 62, p. 225.
L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics: Theory and Application, Ed. by G.-C. Rota, in Encyclopedia of Mathematics and Its Applications (Addison-Wesley, Reading, Mass., 1981).
M. Krawtchouk, Compt. Rend. Acad. Sci. 189, 620 (1929).
K. B. Wolf, Lect. Notes Phys. 352, 115 (1989).
N. M. Atakishiyev, G. S. Pogosyan, and K. B. Wolf, Int. J. Mod. Phys. A 18, 317 (2003).
T. Alieva and K. B. Wolf, J. Opt. Soc. Am. A 17, 1482 (2000).
L. E. Vicent, and K. B. Wolf, J. Opt. Soc. Am. A 25, 1875 (2008).
L. E. Vicent, and K. B. Wolf, J. Opt. Soc. Am. A 28, 808 (2011).
A. R. Urzúa, and K. B. Wolf, J. Opt. Soc. Am. A 33, 642 (2016).
K. B. Wolf, J. Phys. A 41, 304026 (2008).
K. Uriostegui Umaña, Aberraciones ópticas en sistemas discretos y finitos, sobre el espacio fase (Universidad Nacional Autónoma de México, July 2017).
K. B. Wolf, Geometric Optics on Phase Space (Springer-Verlag, Heidelberg, 2004).
K. B. Wolf, J. Math. Phys. 33, 2390 (1992).
S. Steinberg and K. B. Wolf, J. Math. Phys. 22, 1660 (1981).
P. González-Casanova and K. B. Wolf, Num. Meth. Part. Diff. Eq. 11, 77 (1995).
H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, Opt. Commun. 32, 32 (1980).
N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, J. Math. Phys. 39, 6247 (1998).
S. T. Ali, N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, Ann. H. Poincaré 1, 685 (2000).
L. M. Nieto, N. M. Atakishiyev, S. M. Chumakov, and K. B. Wolf, J. Phys. A 31, 3875 (1998).
A. B. Klimov, J. L. Romero, and H. de Guise, J. Phys. A 50, 323001 (2017).
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Wolf, K.B. Optical Models and Symmetries from Finite to Continuous. Phys. Atom. Nuclei 81, 976–979 (2018). https://doi.org/10.1134/S1063778818060327
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DOI: https://doi.org/10.1134/S1063778818060327