What is the structure of 'the strong force'. Let's start with antimatter. First, antimatter is real , not just a mathematical construct to make sense of other particles. Antiquarks have a mass, a charge, and predictable interactions with matter which we can observe. Particles that are made up of quarks are called hadrons , a category that can be further subdivided into mesons and baryons .
Mesons tend to be quark-antiquark pairs with very short lifetimes.
Note, however, that there's no reason three antiquarks can't combine to form a stable antiproton. It's just that in our matter-rich world, such particles don't last long before annihilating with matter. The force that binds quarks and antiquarks together is the strong force , the same force that keeps the protons and neutrons in a nucleus from flying apart. Now on to symmetries. If I throw a baseball off a cliff, and you watch a film of this in reverse, it looks pretty unlikely that the ball would spontaneously rise from the ground up to me.