Yes, there is indeed an analogy between the path integral propagator and the propagators of Feynman diagrams. Both concepts involve the idea of summing over all possible paths or histories.
In the path integral formulation of quantum mechanics, the propagator describes the probability amplitude for a particle to evolve from one state to another over a certain time interval. It is calculated by summing over all possible paths that the particle can take between the initial and final states, and weighting each path by the exponential of the action along that path. The path integral propagator provides a way to compute transition amplitudes and expectation values in quantum mechanics.
On the other hand, Feynman diagrams are graphical representations used in perturbative calculations of quantum field theories, particularly in quantum electrodynamics (QED) and quantum chromodynamics (QCD). Each Feynman diagram represents a contribution to the total amplitude of a particle interaction process. The internal lines in a Feynman diagram represent virtual particles, and the external lines represent the incoming and outgoing particles. The lines in the diagram can be interpreted as propagators, which describe the propagation of particles between interactions.
In this context, each Feynman diagram can be seen as a specific configuration of paths or histories of the interacting particles. The internal lines of the diagram can be understood as a sum-over-paths, where virtual particles can take various trajectories before they interact. The external lines, representing the incoming and outgoing particles, also contribute to the overall amplitude by summing over their possible paths or trajectories.
So, while the path integral propagator and the propagators in Feynman diagrams have different formalisms and contexts, they share a common concept of summing over paths or histories. The propagators in Feynman diagrams represent the contributions of various paths or trajectories of particles within the specific interaction process, whereas the path integral propagator provides a more general framework for calculating transition amplitudes in quantum mechanics.