Lorentz Group applicable to Finite Crystals
Mathematical Physics
2007-05-23 v1 Materials Science
math.MP
Quantum Physics
Abstract
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.
Cite
@article{arxiv.math-ph/0607035,
title = {Lorentz Group applicable to Finite Crystals},
author = {Sibel Baskal and Elena Georgieva and Y. S. Kim},
journal= {arXiv preprint arXiv:math-ph/0607035},
year = {2007}
}
Comments
LaTex 5 pages, presented at 26th International Colloquium on Group Theoretical Methods in Physics (New York, June 2006)