Relativistic Motion

The theory of special relativity replaces the Galilean group with the Poincaré group. This makes the equations of motion of a particle in an external field only slightly more complicated. However, physics at high velocities looks quite different from its nonrelativistic limit.

Newton’s equations, as we know, are only an approximation, and have to be generalized to (1.1.4) or (1.1.6) when the speed of a particle approaches the speed of light. In order to solve these equations in some physically interesting cases, we first put (1.1.4) into Hamiltonian form. This means that the motion takes place in extended configuration space, which is a particular subset of ℝ

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. We shall just concern ourselves with one-body problems, since even when there are only two bodies only special solutions are known if the interaction is relativistic—and therefore not instantaneous (cf. [12]).