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Warning: physically you do not have to change anything, photon still remain 'photon' and electron still remain 'electron'. I'm interested configuring an behavior in particle function exchange, not obtain a new interaction or a new particle.

I want to see what mathematically can come out of it, so physically speaking, more about a way to configure a new possibility to use the same particles, not to generate different information, but activate a way to use that information (particle, charge, interaction..)

So also consider the positron to have charge = $0$

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closed as unclear what you're asking by knzhou, WillO, ZeroTheHero, Dale, John Rennie Nov 18 '18 at 9:54

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    $\begingroup$ So if you don't want to physically give the photon charge, don't want any new interactions, and don't what any particles, what do you actually want to do? $\endgroup$ – knzhou Nov 17 '18 at 23:14
  • $\begingroup$ Aside from any other inconsistencies, the electron would have to emit photons in pairs and would not be able to absorb a photon (assuming charge conservation still holds). So the interaction would be very different, if not impossible, thus making your question not well defined. $\endgroup$ – safesphere Nov 18 '18 at 0:12
  • $\begingroup$ Considering that the electron wouldn't have charge, the positron wouldn't exist as the electron would be it's own anti-particle under charge conjugation, meanwhile as noted above there will exist two photons, one for each charge. $\endgroup$ – Triatticus Nov 18 '18 at 0:40
  • $\begingroup$ @safesphere I try to configure a way to obtain an "electron" or a "photon" from a functional point of view extracted from a context where a homotopy theory has been made and not for doing! (ncatlab.org/nlab/show/model+category). This why I want to freeing the need to have or not have a real or theorically real particle and therefore the dependence on having or not having to use a physical or theoretically physical instrument. In other terms my model can't generating and we don't read and we can not introduce any kind of information, if a new information exist my system fails $\endgroup$ – user332153 Nov 18 '18 at 9:07
  • $\begingroup$ The only thing we can do is to be able to use the same information in a different way but without needing to have it or not to have a information` or not a information ! $\endgroup$ – user332153 Nov 18 '18 at 9:13
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You cannot have a theory like this. It would internally inconsistent. For a gauge boson to carry “charge”, the symmetry group must be nonabelian.

Gluons carry color charge, but the gauge group of the strong interaction is SU(3), which is nonabelian.

Photons cannot carry electric charge because the electromagnetic gauge group is U(1), which is abelian.

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  • $\begingroup$ What would be a non-Abelian group the closest in properties to U(1)? $\endgroup$ – safesphere Nov 18 '18 at 0:05
  • $\begingroup$ @safesphere “Closest in properties” is kind of vague, and abelian-ness (i.e., commutativity) or non-abelian-ness (non-commutativity) is one the most important properties of a group. But I guess I would nominate U(2) as the nonabelian group that is “closest” to U(1). It’s the next group in the same infinite family of general unitary groups. Its close relative SU(2) is one of the gauge groups involved in the electroweak interaction in the Standard Model. Because it is nonabelian, W and Z bosons interact directly with each other, like gluons do but unlike photons. $\endgroup$ – G. Smith Nov 18 '18 at 3:14

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