A Note on analytic formulas of Feynman propagators in position space
Hong-Hao Zhang, Kai-Xi Feng, Si-Wei Qiu, An Zhao, Xue-Song Li
TL;DR
This paper corrects previous inaccuracies and derives generalized analytic formulas for Feynman propagators in position space across arbitrary dimensions, revealing recurrence relations among different dimensional propagators.
Contribution
It provides corrected and generalized formulas for scalar and spinor Feynman propagators in arbitrary (D+1)-dimensional spacetime, including recurrence relations.
Findings
Corrected previous inaccuracies in Feynman propagator formulas.
Derived generalized formulas for arbitrary dimensions.
Discovered recurrence relations among propagators in different dimensions.
Abstract
In this paper, we correct an inaccurate result of previous works on the Feynman propagator in position space of a free Dirac field in (3+1)-dimensional spacetime, and we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary (D+1)-dimensional spacetime, and we further find a recurrence relation among the spinor Feynman propagator in (D+1)-dimensional spacetime and the scalar Feynman propagators in (D+1)-, (D-1)- and (D+3)-dimensional spacetimes.
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