A transformation $\Lambda$ is a Lorentz transformation if it satisfies $\Lambda^T g \Lambda = g$, for the flat metric $g = \left( \begin{array}{cccc} 1 &&& \\ & -1 &&& \\ &&-1&& \\ &&&-1 \end{array} \right) $

In addition to rotations and boosts, time reversal ($T: t \rightarrow -t$) and parity ($P: x_i \rightarrow -x_i$ for all spatial coordinates) are singled-out as discrete Lorentz transformations. I find that reversal of a single spatial coordinate ($x_1 \rightarrow -x_1$, all others unchanged) also satisfies the definition of a Lorentz transformation. So the question is: why isn't it considered as another discrete transformation, alongside $T$ and $P$?

A transformation $\Lambda$ is a Lorentz transformation if it satisfies $\Lambda^T g \Lambda = g$, for the flat metric $$g = \left( \begin{array}{cccc} 1 &&& \\ & -1 &&& \\ &&-1&& \\ &&&-1 \end{array} \right) .$$

In addition to rotations and boosts, time reversal ($T: t \rightarrow -t$) and parity ($P: x_i \rightarrow -x_i$ for all spatial coordinates) are singled-out as discrete Lorentz transformations. I find that reversal of a single spatial coordinate ($x_1 \rightarrow -x_1$, all others unchanged) also satisfies the definition of a Lorentz transformation. So the question is: why isn't it considered as another discrete transformation, alongside $T$ and $P$?

A transformation $\Lambda$ is a Lorentz transformation if it satisfies $\Lambda^T g \Lambda = g$, for the flat metric $g = \left( \begin{array}{cccc} 1 &&& \\ & -1 &&& \\ &&-1&& \\ &&&-1 \end{array} \right) $

In addition to rotations and boosts, time reversal ($T: t \rightarrow -t$) and parity ($P: x_i \rightarrow -x_i$ for all spatial coordinates) are singled-out as discrete Lorentz transformations. I find that reversal of a single spatial coordinate ($x_1 \rightarrow -x_1$, all others unchanged) also satisfies the definition of a Lorentz transformation. So the question is: why isn't it considered as another discrete transformation, alongside $T$ and $P$?

A transformation $\Lambda$ is a Lorentz transformation if it satisfies $\Lambda^T g \Lambda = g$, for the flat metric $g = \left( \begin{array}{cccc} 1 &&& \\ & -1 &&& \\ &&-1&& \\ &&&-1 \end{array} \right) $

In addition to rotations and boosts, time reversal ($T: t \rightarrow -t$) and parity ($P: x_i \rightarrow -x_i$ for all spatial coordinates) are singled-out as discrete Lorentz transformations. I find that reversal of a single spatial coordinate ($x_1 \rightarrow -x_1$, all others unchanged) also satisfies the definition of a Lorentz transformation. So the question is: why isn't it considered as another discrete transformation, alongside $T$ and $P$?