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Add fermion exchange logic and tests for bhabha scattering #37

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AntonReinhard
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Currently only tested for n-Photon Compton processes (where it changes nothing) and Bhabha scattering (e- e+ -> e- e+).

Fixes #27

@AntonReinhard AntonReinhard force-pushed the fermion-exchange-negation branch 2 times, most recently from 7a001d7 to 0768837 Compare November 1, 2024 12:53
@AntonReinhard AntonReinhard force-pushed the fermion-exchange-negation branch from 0768837 to 954f979 Compare November 1, 2024 13:52
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Okay I found that this does work for n=1 and n=2 fermion lines, but stops working beyond that, as I feared/expected.

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I implemented a new algorithm where the VirtualParticles now also carry information about the remaining open cycles of their subdiagrams. Negation then happens on Pair and Triples tasks, once for every cycle that closes. Because the cayley distances of permutations can be calculated by n-number_of_cycles in a permutation, this comes out to the same when we only care about whether an even or odd amount of transactions are necessary.
I will write some actual documentation on how all of this works at some point, too. And also, hopefully, some more formal proof that it is correct.

@AntonReinhard AntonReinhard force-pushed the fermion-exchange-negation branch from 5dbca81 to 46a5753 Compare January 2, 2025 12:41
@AntonReinhard AntonReinhard marked this pull request as ready for review January 2, 2025 12:43
@AntonReinhard AntonReinhard merged commit 3420bde into QEDjl-project:dev Jan 2, 2025
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@AntonReinhard AntonReinhard deleted the fermion-exchange-negation branch January 2, 2025 14:01
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Fix relative negation of terms for exchangable fermions
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