What is the physical interpretation of Feynman's path integral formulation of quantum mechanics?
The Feynman Path Integral (FPI) provides a way to calculate the probability of a certain outcome in quantum mechanics by summing over all possible paths that lead from an initial state to a final state. The idea behind this approach is that if we can accurately describe the behavior of a system through a series of small steps, then we can also approximate its overall evolution by summing over all possible sequences of these steps.

In terms of its physical interpretation, the FPI describes the motion of particles as a random walk on a graph, where each step represents a possible interaction between the particle and its environment. By summing over all possible pathways, the FPI allows us to account for both the coherent effects of interactions with the wavefunction and the random fluctuations due to environmental noise. This gives us a more complete picture of how particles behave in quantum systems, and it has been used to study a wide range of phenomena, including the dynamics of atoms and molecules, the transport of electrons in metals, and the behavior of superconducting circuits.

Overall, the FPI is considered one of the most successful approaches to understanding quantum mechanics, and it continues to play an important role in our understanding of many complex physical systems.