Gluon creation and annihilation operators

[Paul Colby]

Hi,

When one quantizes EM the resulting gauge boson, the photon, ends up being its own antiparticle. From what I read of gluons, they have anti particles. I can follow how anti particles come about quantizing a complex-valued field like that for electrons. For the spin 1/2 case non-interacting fields are sums of particle - anti particle annihilation operators. How does this end up working for the gluon case which are 8 spin 1 real-valued fields?

 

[mathman]

https://www.quora.com/What-are-the-antiparticles-of-gluons

anti-particles of gluons are other gluons.

 

[Paul Colby]

Okay, thanks. I think I get it maybe kind of. Has it to do with how one defines color charge? The real fields $G_{a}^{\mu}$ are just like the case with photons, the sum of a creation and annihilation operators but they don't create or annihilate pure color charge states?

 

[mathman]

Sorry - I don't any more than what is in the reference.

 

[Paul Colby]

The reference is helpful and I believe I now understand "better". I'm still digesting it. The $G_a^\mu$ fields are Hermitian and therefore are the sum of a boson creation operators and their conjugates (annihilation) operators, at least in the linear limit. The challenge for me is to understand what an "opposite" color charge means arithmetically, since color charge is not just a number like electric charge but some funky vector matrix thing. Thanks for the link. It is quite helpful.