19 citations · 166 across the 26 of their papers we have counts for
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Wigner's Space-time Symmetries based on the Two-by-two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
Sibel Baskal, Young S. Kim, Marilyn E. Noz
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group $Sp…
One analytic form for four branches of the ABCD matrix
S. Baskal, Y. S. Kim
It is not always possible to diagonalize the optical matrix, but it can be brought into one of the four Wigner matrices by a similarity transformation. It is shown that the…
ABCD Matrices as Similarity Transformations of Wigner Matrices and Periodic Systems in Optics
S. Baskal, Y. S. Kim
The beam transfer matrix, often called the matrix, is a two-by-two matrix with unit determinant, and with three independent parameters. It is noted that this matrix cannot a…
Diagonalization of Sp(2) matrices
S. Baskal, Elena Georgieva, Y. S. Kim
The two-by-two Sp(2) matrix has three parameters with unit determinant. Yet, there are no established procedures for diagonalizing this matrix. It is shown that this matrix can be…
Lorentz Group applicable to Finite Crystals
Sibel Baskal, Elena Georgieva, Y. S. Kim
The two-by-two scattering matrix for one-dimensional scattering processes is a three-parameter Sp(2) matrix or its unitary equivalent. For one-dimensional crystals, it would be rep…
Rotations associated with Lorentz boosts
S. Baskal, Y. S. Kim
It is possible to associate two angles with two successive non-collinear Lorentz boosts. If one boost is applied after the initial boost, the result is the final boost preceded by…
Wigner's new physics frontier: Physics of two-by-two matrices, including the Lorentz group and optical instruments
Sibel Baskal, Elena Georgieva, Y. S. Kim
According 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 wit…
Lens optics as an optical computer for group contractions
S. Baskal, Y. S. Kim
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 analy…
Wigner Rotations in Laser Cavities
S. Baskal, Y. S. Kim
The Wigner rotation is a key word in many branches of physics, chemistry and engineering sciences. It is a group theoretical effect resulting from two Lorentz boosts. The net effec…