Lorentz group is the language of special relativity, while the harmonic oscillator is one of the major tools for interpreting bound states. Therefore, Dirac’s two-oscillator system can serve as a mathematical framework for understanding quantum bound systems in the Lorentz-covariant world.

Within this formalism, the series given in Eq.(\[seri00\]) can be produced from the ten-generator Dirac system. In discussing the oscillator system, the standard procedure is to use the normal coordinates defined as $$\label{norm00}
u = \frac{x + y}{\sqrt{2}}, \quad\mbox{and}\quad v = \frac{x - y}{\sqrt{2}}.$$ In terms of these variables, the transformation given in Eq.(\[sq01\]) takes the form $$\label{sq02}
\pmatrix{u' \cr v'} = \pmatrix{e^{-\eta} & 0 \cr
   0 & e^{\eta}}
  \pmatrix{u \cr v} ,$$ where this is a squeeze transformation along the normal coordinates. While the normal-coordinate transformation is a standard procedure, it is interesting to note that it also serves as a Lorentz boost [@dir49].

With these preparations, we shall study in Sec. \[2dim\], the system of two oscillators and coordinate transformations of current interest. It is pointed out in Sec. \[dirac63\] that there are ten different generators for transformations, including those discussed in Sec. \[2dim\]. It is noted that Dirac derived ten generators of transformations applicable to these 