What Does Path Mean in Quantum Mechanics and Quantum Field Theory?

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In quantum mechanics (QM) and quantum field theory (QFT), the concept of a particle's path is fundamentally different from classical mechanics due to the uncertainty principle. Richard Feynman's path integral formulation provides a probabilistic approach that enhances predictive accuracy, but the precise definition of a path remains ambiguous. Quantum entanglement further complicates path descriptions by imposing limitations on information transfer speed. In modern physics, a path can refer to the trajectory of a particle's center of mass or, in the case of waves, the trajectory of the phase center where a specific phase value is observed. Understanding these concepts is crucial for grasping the complexities of quantum behavior.
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What is a Path in QM and QFT ?

In classical mechanics, we are allowed to talk about path of a particle. But in quantum mechanics, the concept of path of a particle cannot be defined. This is due to the uncertainty principle.

But Feynman talked about path integral in quantum mechanics. This probabilty integral gives more accurate prediction than any other theory. Yet the meaning of path is still not clearly defined. Then quantum entanglement also does not allow path description because of its limit of luminal speed.

What is the meaning of path in modern physics?
 
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A path in quantum physics is a trajectory of a particle or a wave. In the case of a particle, the path is the trajectory of the center of mass. In the case of a wave, the path is a trajectory of the phase center, which is the location at which the wave has a specified phase value.
 

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