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- TL;DR Summary
- Confusing interaction between matter and antimatter in Dirac equation.

I'm new to relativistic quantum mechanics and quantum field theory and was trying to learn about the Dirac equation.

Unfortunately, I got a little stumped by the interaction between matter and antimatter.

It seems like the time derivative of matter is dependent on the spatial derivative of antimatter, but not the spatial derivative of matter. Likewise, the time derivative of antimatter is dependent on the spatial derivative of matter, but not the spatial derivative of antimatter.

To me this means that if there is momentum of matter, then the antimatter field should be changing, which doesn't make sense to me.

I find this counterintuitive and was hoping that someone could explain this to me.

Unfortunately, I got a little stumped by the interaction between matter and antimatter.

It seems like the time derivative of matter is dependent on the spatial derivative of antimatter, but not the spatial derivative of matter. Likewise, the time derivative of antimatter is dependent on the spatial derivative of matter, but not the spatial derivative of antimatter.

To me this means that if there is momentum of matter, then the antimatter field should be changing, which doesn't make sense to me.

I find this counterintuitive and was hoping that someone could explain this to me.