Yet, the Gaussian form of Eq.(\[gau33\]) appears to be a rotated squeezed state, while not along the normal coordinates. We shall look at this problem in detail in Sec. \[shear\].

Dirac’s Entangled Oscillators {#dirac63}
=============================

Paul A. M. Dirac devoted much of his life-long efforts to the task of making quantum mechanics compatible with special relativity. Harmonic oscillators serve as an instrument for illustrating quantum mechanics, while special relativity is the physics of the Lorentz group. Thus, Dirac attempted to construct a representation of the Lorentz group using harmonic oscillator wave functions [@dir45; @dir63].

In his 1963 paper [@dir63], Dirac started from the two-dimensional oscillator whose wave function takes the Gaussian form given in Eq.(\[gau00\]). He then considered unitary transformations applicable to this ground-state wave function. He noted that they can be generated by the following ten Hermitian operators $$\begin{aligned}
\label{dir10}
&{}& L_{1} = {1\over 2}\left(a^{\dag} b + b^{\dag} a\right) ,\qquad
L_{2} = {1\over 2i}\left(a^{\dag} b - b^{\dag} a\right) ,  \nonumber \\[3mm]
&{}& L_{3} = {1\over 2}\left(a^{\dag} a - b^{\dag} b \right) , \qquad
S_{3} = {1\over 2}\left(a^{\dag}a + bb^{\dag}\right) ,   \nonumber \\[3mm]
&{}& K_{1} = -{1\over 4}\left(a^{\dag}a^{\dag} + aa - b^{\dag}b^{\dag} - bb\right) , \nonumber \\[3mm]
&{}& K_{2} = 