Wigner's new physics frontier: Physics of two-by-two matrices, including the Lorentz group and optical instruments

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dc.creatorBaskal, Sibel
dc.creatorGeorgieva, Elena
dc.creatorKim, Y. S.
dc.date2003-10-31
dc.date.accessioned2026-07-07T04:30:42Z
dc.date.available2026-07-07T04:30:42Z
dc.descriptionAccording to Eugene Wigner, quantum mechanics is a physics of Fourier transformations, and special relativity is a physics of Lorentz transformations. Since two-by-two matrices with unit determinant form the group SL(2,c) which acts as the universal covering group of the Lorentz group, the two-by-two matrices constitute the natural language for special relativity. The central language for optical instruments is the two-by-two matrix called the beam transfer matrix, or the so-called ABCD matrix. It is shown that the ABCD matrices also form the SL(2,C) group. Thus, it is possible to perform experiments in special relativity using optical instruments. Likewise, the optical instruments can be explained in terms of the symmetry of relativistic particles.
dc.descriptionLatex 28 pages, based on the papers presented by the last author(YSK) at a number of conferences, including the 8th International Wigner Symposium (New York, U.S.A., 2003), the 8th International Conference on Squeezed States and Uncertainty Relations (Puebla, Mexico, 2003), the Symmetry Festival (Budapest, Hungary, 2003), and the International Conference on Physics and Control (Saint Petersburg, Russia, 2003)
dc.identifierhttps://arxiv.org/abs/math-ph/0310068
dc.identifierhttp://arxiv.org/abs/math-ph/0310068
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57550
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Physics
dc.titleWigner's new physics frontier: Physics of two-by-two matrices, including the Lorentz group and optical instruments
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