Diagonalization of Sp(2) matrices

Abstract

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 written as a similarity transformation of the two-by-two Wigner matrix, derivable from Wigner's little group which dictates the internal space-time symmetries of relativistic particles. The Wigner matrix can be diagonalized for massive and space-like particles, while it takes a triangular form with unit diagonal elements for light-like particles. The most immediate physical application can be made to repeated one-dimensional transfer matrices appearing in many different branches of physics. Another application of current interest could be the dis-entanglement of entangled systems.