quantum information. Earlier, this formula played the pivotal role for Yuen to formulate his two-photon coherent states or two-mode squeezed states [@yuen76]. The same formula was used by Yurke and Patasek in 1987 [@yurke87] and by Ekert and Knight [@ekert89] for the two-mode squeezed state where one of the photons is not observed. The effect of entanglement is to be seen from the beam splitter experiments [@paris99; @mskim02].

In this paper, we point out first that the series of Eq.(\[seri00\]) can also be written as a squeezed Gaussian form $$\label{i01}
\frac{1}{\sqrt{\pi}}
              \exp{\left\{-\frac{1}{4}\left[e^{-2\eta}(x + y)^2 +
               e^{2\eta}(x - y)^{2}\right]\right\}} ,$$ which becomes $$\label{i02}
\frac{1}{\sqrt{\pi}}
              \exp{\left\{-\frac{1}{2}\left(x^2 + y^2\right)\right\}} ,$$ when $\eta = 0$.

We can obtain the squeezed form of Eq.(\[i01\]) by replacing $x$ and $y$ by $x'$ and $y'$ respectively, where $$\label{sq01}
\pmatrix{x' \cr y'} = \pmatrix{\cosh\eta
& -\sinh\eta \cr -\sinh\eta & \cosh\eta}
\pmatrix{x \cr y} .$$ If $x$ and $y$ are replaced by $z$ and $t$, Eq.(\[sq01\]) becomes the formula for the Lorentz boost along the $z$ direction. Indeed, the Lorentz boost is a squeeze transformation [@kn05job; @hkn90].

The squeezed Gaussian form of Eq.(\[i01\]) plays the key role in studying boosted bound states in the Lorentz-covariant world [@dir27; @dir45; @dir49; 