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Lens optics as an optical computer for group contractions | | S. Baskal
; Y. S. Kim
; | | Date: |
30 Oct 2002 | | Journal: | Phys. Rev. E 67 (2003) 56601 | | Subject: | Mathematical Physics; Optics | math-ph hep-th math.MP physics.optics quant-ph | | Abstract: | It is shown that the one-lens system in para-axial optics can serve as an optical computer for contraction of Wigner’s little groups and an analogue computer which transforms analytically computations on a spherical surface to those on a hyperbolic surface. It is shown possible to construct a set of Lorentz transformations which leads to a two-by-two matrix whose expression is the same as those in the para-axial lens optics. It is shown that the lens focal condition corresponds to the contraction of the O(3)-like little group for a massive particle to the E(2)-like little group for a massless particle, and also to the contraction of the O(2,1)-like little group for a space-like particle to the same E(2)-like little group. The lens-focusing transformations presented in this paper allow us to continue analytically the spherical O(3) world to the hyperbolic O(2,1) world, and vice versa. | | Source: | arXiv, math-ph/0210056 | | Services: | Forum | Review | PDF | Favorites | |
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