(adsbygoogle = window.adsbygoogle || []).push({}); 4-velocity "length" under a force

In relativity we have [tex]u^\mu u_\mu=c^2[/tex], which is just another way of saying that [tex]p^\mu p_\mu=m^2c^2[/tex] or [tex]E^2=m^2c^4+p^2c^2[/tex].

This is relatively (no pun!) easy to see for a free particle. But if we have a vector potential acting on the particle, is the above still true? Or do we have instead that

[tex](p_\mu +qA_\mu)(p^\mu+qA^\mu)= constant[/tex]

?

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# 4-velocity length under a force

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