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] ?