oscillators, and they satisfy the closed set of commutation relations which is the same as the Lie algebra of the $O(3,2)$ de Sitter group containing two Lorentz groups among its subgroups. In Sec. \[wigf\], Dirac’s ten-generator symmetry is studied in the Wigner phase-space picture, and it is shown that Dirac’s symmetry contains both canonical and Lorentz transformations.

While the Gaussian entanglement starts from the oscillator wave function in its ground state, we study in Sec. \[excited\] the entanglements of excited oscillator states. We give a detailed explanation of how the series of Eq.(\[seri00\]) can be derived from the squeezed Gaussian function of Eq.(\[i01\]).

In Sec. \[shear\], we study in detail how the sheared state can be derived from a squeezed state. It appears to be a rotated squeezed state, but this is not the case. In Sec. \[restof\], we study what happens when one of the two entangled variables is not observed within the framework of Feynman’s rest of the universe [@fey72; @hkn99ajp].

In Sec. \[spt\], we note that most of the mathematical formulas in this paper have been used earlier for understanding relativistic extended particles in the Lorentz-covariant harmonic oscillator formalism [@kn73; @knp86; @kno79jmp; @kno79ajp; @kiwi90pl; @kn11symm]. These formulas 