Lorentz Group applicable to Finite Crystals

Details Lorentz Group applicable to Finite Crystals Lorentz Group applicable to Finite Crystals

2006-07-18

arxiv.org/abs/math-ph/0607035v1

Physics

Mathematical Physics

LaTex 5 pages, presented at 26th International Colloquium on Group Theoretical Methods in Physics (New York, June 2006)

Scientific paper

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 repeated applications of this matrix. The problem is how to calculate N repeated multiplications of this matrix. It is shown that the original Sp(2) matrix can be written as a similarity transformation of Wigner's little group matrix which can be diagonalized. It is then possible to calculate the repeated applications of the original Sp(2) matrix.

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