Energy-Momentum 4-Vector

         The invariance of "length" of this 4-Vector is associated with the fact that the rest mass of a particle is invariant under coordinate transformation.

            This ca be defined through the velocity 4-Vector:

 or                    (21)

where m0 is the particle rest mass and .

The length of the energy-momentum 4-Vector is given by:

              (22)

and represents the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame. This relation is also true for mass-less particles, such as the photons, for which E=pc or p=E/c. These ones are related to a frequency n and wavelength l:

 

         and            

            The Lorentz transformation can be expressed in matrix form:

           (23)

Thus:

              (24)

 

One can use these expressions in particle physics, to obtain a particle momentum and energy in the center-of-mass frame according to those in the laboratory frame.

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