I'm reading "Teaching Feynman’s sum-over-paths quantum theory" by Taylor et al.(adsbygoogle = window.adsbygoogle || []).push({});

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.374.4480&rep=rep1&type=pdf,

I'd like to confirm whether my understanding is correct, so a couple of questions.

1.We need to try and think of all kinds of different classical, not-quite-classical, and frankly weird trajectories that are going to contribute to the final "arrow" (propagator?).Buthave to restrict ourselves to trajectories that complete the trip from A to B in the same time as that of a straight line flight from A to B. -- Is this correct?

2.Once we select a path, we integrate the difference between KE and PE along that path. How do we calculate this for a photon if we consider a segment where it is flying, say, at 2 xc?

3.Consider an interferometer in a laboratory. There is a detector where we see a complete null due to destructive interference. Now on another workbench is a mirror that has nothing do do with the experiment at all. But based on the nature of diffraction and gaussian beams (which have an inevitable "tail" that never goes to zero) we know that if we move that mirror, there will be a tiny change in the position of the null because some non-zero part of the energy bounces off that unused mirror. Now my question is, when we consider 'non-classical' Feynman paths that bounce off that stray mirror, is this merely a way of including weak diffraction contributions, or is there something way deeper going on?

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# I Feynman path integral

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