[talanum1 (OP)]

Quantum Field Theory says that the Electron and Positron Fields fill all space. Do they therefore cancel?

If yes, how would the Electron field then know to produce an Electron?

[Bored chemist]

Do they therefore cancel?

No.

[Kryptid]

Bored Chemist is right. An electron is an excitation of the electron field. When an electron is present, all that means is that there is no excitation of the positron field at that same place.

EDIT: Or, I think the electron field and positron field may be the same thing. At least, I think I was corrected on that at one point in time. I guess that would make electrons and positrons "opposite" excitations of the same field.

[Kartazion]

Quantum Field Theory says that the Electron and Positron Fields fill all space. Do they therefore cancel?

The excitation created or destroyed the particle. From another perspective it is preferable to speak of annihilation of electron and positron. Finally gamma photons are made of it.

[Kartazion]

EDIT: Or, I think the electron field and positron field may be the same thing. At least, I think I was corrected on that at one point in time. I guess that would make electrons and positrons "opposite" excitations of the same field.

The similarity of the two fields between electron and positron is beyond doubt. Its distinction between e+ and e- is situated at the symmetry breaking supplementary to the CP when the particle therefore oscillates between matter and antimatter through an an/harmonic oscillator.