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In The Feynman lectures on physics volume 3, chapter 3, page 3-11, there is the following paragraph:

An even more perplexing thing happens when we do the same kind of experiment by scattering electrons on electrons, and protons on protons... For these particles, we must invoke still a new rule, a most peculiar, which is the following: when you have a situation in which the identity of the electron which is arriving at a point is exchanged with another one, the new amplitude interferes with the old one with an opposite phase.

Until this point in the book, we deal only with positive interference, and I didn't quite get negative interference. I suspect the reason why electrons negatively interfere but alpha particles positively interfere is in the above paragraph, but I am not able to comprehend it.

Thank you.

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This refers to the Feynman rule that crossing fermionic lines produce relative minus signs between amplitudes. That is, if you have some process that is mediated by two different Feynman graphs and one graph is obtained from the other through an odd number exchanges of fermionic endpoints, you must subtract instead of add the amplitudes corresponding to these graphs.

Heuristically, this has to do with the Pauli exclusion principle and the fermionic creation operators anticommuting instead of commuting, formally you have to step through the LSZ or interaction picture derivation of the Feynman rules in order to see the origin of this rule.

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  • $\begingroup$ I'm a high school student whose only background on quantum is the previous two chapters the book. I didn't understand anything in this answer. Is there a simple (even if imprecise or rough) explanation? I'll come back and try to understand this when I've studied more. $\endgroup$ – Mahathi Vempati Jun 7 '16 at 15:57

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