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Is it just charge that causes particles to have an antiparticle?


No. Neutrons and antineutrons are different particles, for example.


Neutrons don't have charge, but their quarks do. Antineutrons have quarks with reversed charge.

Just like a neutral atom can have a neutral antiatom.


If you prefer, then, neutrinos are neutral but have an anti-particle (although it's still possible that neutrinos are Majorana particles, in which case they're their own anti-particle).




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