# Complex conjugation between particle/ anti-particle?

I am just a first year undergrad so I don't really know much about particle physics or the underlying mathematics. So I'm very sorry if the following question may be just stupid :D

So I noticed that antiparticles in Feynman diagrams are often presented by a bar over the letter, i.e. a quark $$q$$ and an anti-quark $$\bar{q}$$. This bar is often used in mathematics to denote the complex conjugation of a complex number.

My question now is: Are the mathematical objects by which particles and their anti-particles are described (by the way what are these objects?) anyhow related to each other by some operation that has something to do with complex conjugation or is it just coincidence?

Once again, I am sorry if this question is obsolete or something. Either way I would very much appreciate an answer!

• possibly useful : physics.stackexchange.com/q/390342 – Slereah Sep 3 '19 at 13:54
• It’s not a coincidence. Complex numbers and complex conjugation appear throughout quantum mechanics and thus particle physics. – G. Smith Sep 3 '19 at 16:16

Quarks are fermions, which are represented by a Dirac spinor $$q$$ in QFT. The overbar denotes the Dirac adjoint, which is defined as $$\bar{q}=q^{\dagger}\gamma^{0}$$, where $$\dagger$$ denotes Hermitian conjugate, and $$\gamma^{0}$$ is the timelike gamma maxtrix.