Squeeze operator: a classical view

Abstract

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.