- #1
spaghetti3451
- 1,344
- 34
Consider the Heaviside function ##\Theta(k^{0})##.
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?
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?