The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic action) but many of them are relativistic or physically impossible because the velocity had to be larger than the speed of light. So why are we doing so? Why do we also count the paths where the particle must be viewed as relativistic but still weight it with the non-relativistic action? And why sum we over the paths where the particle must move faster then the speed of light?
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