A few things are known about quantum fields. One; electrons are fermions, in which fermions cannot exist in the same state at the same time. And two; this is because particles with antisymmetric wave patterns cannot exist in the same state. According to quantum field theory, electrons must have antisymmetric wave patterns in quantum fields because if the fields are annotated as spin-0 and no spin- ½ this shows that electrons must have antisymmetric wave patterns otherwise there would be an infinity number of negative energy states.

This concept is explained in the Peskin and Schroder proof, and by using the Lorentz invariant. It all comes down to the mathematical symmetric equations, such as the C symmetry. In short, electrons must have antisymmetric wave patterns, since their bison counterparts are symmetric. Bosons can occupy the same state, while fermions cannot. This balance is required to establish the behavior of an atom