Consider the Heaviside function ##\Theta(k^{0})##.(adsbygoogle = window.adsbygoogle || []).push({});

This function is Lorentz invariant if ##\text{sign}\ (k^{0})## is invariant under a Lorentz transformation.

I have been told that only orthochronous Lorentz transformations preserve ##\text{sign}\ (k^{0})## under the condition that ##k## is a time-like vector.

I would like to prove this explicitly, to convince myself of the fact. How do I start?

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# A Lorentz invariance of the Heaviside function

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