Special Relativity | Part IB, 2004

State how the 4 -momentum pμp_{\mu} of a particle is related to its energy and 3momentum. How is pμp_{\mu} related to the particle mass? For two particles with 4 -momenta p1μp_{1 \mu} and p2μp_{2 \mu} find a Lorentz-invariant expression that gives the total energy in their centre of mass frame.

A photon strikes an electron at rest. What is the minimum energy it must have in order for it to create an electron and positron, of the same mass mem_{e} as the electron, in addition to the original electron? Express the result in units of mec2m_{e} c^{2}.

[It may be helpful to consider the minimum necessary energy in the centre of mass frame.]

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