A New Relativistic Mechanics for Two-Particle System

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Abstract
We present a new theory for two relativistic particles interacting through an action-at-a-distance force. The masses of the constituent particles are well defined. We treat the equal and unequal mass cases simultaneously. In the interaction case we get the conditions which suppress the internal time component in the rest-frame. Using the conditions as strong equations, we quantize the system canonically. A generalized Klein-Gordon equation is obtained. The internal space is three-dimensional and Euclidian but the wave equation is Lorentz covariant. The harmonic oscillator system is solved. The leading Regge trajectory is linear rising in the case of the equal constituent mass. In the unequal mass case, however, it has a leap in an unphysical region and deviate from a straight line near the leap. The extent of the leap and the deviation depends on the value of the mass- difference of the constituent particles.

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