= Proper orthochronous Lorentz transformation
{title2=$\Lambda\in SO^+(1,3)$}
A <Lorentz transformation> with <determinant> $+1$ that preserves future-directed timelike <four-vectors>. Equivalently, it belongs to the identity component of the <Lorentz group>. For the <Minkowski metric> $(-,+,+,+)$, its <matrix> satisfies $\Lambda^T\eta\Lambda=\eta$ and $\Lambda^0{}_0\ge1$. Such transformations preserve the future <light cone>, so the <retarded Green function> of the <d'Alembert operator> transforms as a <Lorentz scalar>.
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