In this paper we show the relation between $sp(4,\mathbb{ R})$, the Lie algebra of the symplectic group, and the elements of the symplectic group $Sp(4,\mathbb{ R})$. We use this relation to provide a classical analog of the squeeze operator $\widehat{ S}(\zeta)$. This classical squeeze matrix shares some similarities with the correlation matrix ${ \bf V}^{ (2)}$ and its amount of squeezing is half of that in the correlation matrix.
Categories: math-ph math.MP