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Physicist here. You are confusing things. Having rest mass or Pauli-exclusion principle has nothing to do with qualification of being an anti-particle.

Z boson, for instance, does have mass and is its own anti-particle.

It's basically like saying "the number 0 is its own negative number". It's correct according to some definitions, but not useful.

Photons have zero charge; an anti-particle has negative of the particle's charge (and at the same time, same rest mass and spin).

Aha, thanks for the correction, I must have picked up some bad info somewhere. I'll do my research better next time.

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