Why don't photons annihilate with themselves if they're their own antimatter?

[Haibara Ai]

If photons are their own antimatter, then why don't they just annihilate? Also, do neutrons have antimatter, or is it themselves?

 

[malawi_glenn]

The very requirement for antiparticle is not that they annihilate.
Antiparticles is just the opposite charge and spin (time reversed particle), and SOME antiparticles will annihilate if they interact with each other. Now in standard QED, photon-photon interactions is not possible (at least not with a virtual photon coupling, but with several virtual electron/positrons)
see http://universe-review.ca/R15-12-QFT.htm

So in one sense two photons will annihilate and form photons again ;-)

I mean, what is meant by annihilation in physics anyway?

The antiparticle of the neutron is the antineutron, which has the constituent anti-quarks of the neutron, eg. 2 anti-down, 1 anti-up

 

[Haibara Ai]

That makes sense...
Thanks!