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Example: electron positron annihilation forbids a single photon production, and searching through this forum (Why can't a single photon produce an electron-positron pair?) and a few books, they always reason with this by using the centre of mass frame of reference where the two incoming bodies $e^{+}$ and $e^{-}$ have equal and opposite momentum, hence due to conservation of energy and momentum the final state (photon) cannot exist since a photon with no momentum is impossible.

However considering a frame of reference - stationary - at the point of collision of an electron and a positron incoming at a 90 degree angle to each other, what forbids a single photon production?

Qmechanic
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magnificent_wts
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1 Answers1

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You can use any frame you want. If something is forbidden, it is forbdden in all frames. The math is generally easiest in the center-of-mass frame... sometimes so easy that the impossibility of a reaction is obvious. The reason why is that by choosing this frame you have already satisfied one of the conservation laws.

G. Smith
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