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But i got a question, I want to define velocity, momentum and energy. These looks like a simple task but let me explain the problem.

I'm working in the Minkowski space, and the lorentz transformations (just geometrical one's) and i can only use geometrical arguments.

For example, if we got a lorentz transformation, we could define the velocity of the frame of reference (respect one that is quite, like a lab) as

u_i = -delta_i^4/delta_4^4

where delta^j_i is the (j,i) coeficient of the lorentz transformation.

(Extract from The Geometry of Minkowski spacetime. Naber. Springer-Verlag)

I'm completly sure these work it could be found at wikipedia (some time ago i found it there) but i dont know why i can't find it now.

If somebody could help me I will be very pleased, if you only read this thanks anyway.

(sorry if my english is not good enough)