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 $\hat{S}(\zeta )$. This classical squeeze matrix shares some similarities with the correlation matrix ${\mathbf{V}}^{(2)}$ and its amount of squeezing is half of that in the correlation matrix.

14 pages, 2 figures

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• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Polymer Quantum Mechanics and its Continuum Limit
• Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology
• The symplectic group in Polymer Quantum Mechanics