General Expression for the Interaction Energy

In order to calculate the interaction energy of particles 1 and 2 we need to transform these potentials to the original frame of reference IS by the inverse Lorentz boost as given by Eqs. (3.81) and (3.82), 

The interaction energy V 2 ti) is very involved because of the lengthy expression of (p2 defined in Eq. (3.211), which contains the velocity of charge 2 as well as two different times ti and (2 in the denominator (which would create insurmountable difficulties upon a later transition to quantum mechanics by relying on the correspondence principle). Therefore, it is desirable to calculate the interaction energy solely from quantities defined at fi (and not at (2)- 

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