Regular Article - Theoretical Physics
The stepwise path integral of the relativistic point particle
Instituto de Física, Pontificia Universidad Católica de Chile, Casilla 306, Santiago, Chile
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Accepted: 22 March 2018
Published online: 2 April 2018
In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman–Kolmogorov relation, can be solved by a careful analysis of the overcounting associated with local and global symmetries. Based on this, the direct calculation of the quantum propagator of the relativistic point particle in the path integral formulation results from a simple and purely geometric construction.
© The Author(s), 2018