# Do distinguishable fermions obey the Pauli exclusion principle?

We know that fermions are identical particles and obey Pauli exclusion principle. But what is meant by distinguishable fermions? Does that mean, like proton and electron both are fermions but they are distinguishable because of charge? And if we put together both distinguishable fermions, will they obey Pauli exclusion principle ?

• You may want to fix the first sentence, as it seems to assert that fermions are indistinguishable by definition, which makes the rest of the question difficult to parse. Sep 27, 2018 at 11:58

The simple way to think about it is to imagine that all fermions are excitations of a single field. These excitations can differ in their position, spin, charge, mass, and so on, and the Pauli exclusion principle applies to all of them. Mathematically, this is just the fact that all fermionic creation operators anticommute; the joint wavefunction of all fermions is antisymmetric.

So fermions that are far apart aren't affected, because they differ in position space. Fermions that have different spins aren't affected, because they differ in spin. And protons and neutrons don't affect each other because they differ in mass and charge. The Pauli exclusion principle always applies and there are no exceptions. Any two fermions must be different in some way to coexist.

Because spin and position are easily changed, and mass and charge aren't, sometimes people break the rule into two cases. They say that Pauli exclusion only looks at spin and position, and doesn't apply to things with different masses and charges (because they're automatically different). This works for simple situations, but it's dangerous, because if you take it too literally you'll get the wrong answer when constructing baryon wavefunctions. There you really do have to antisymmetrize over all degrees of freedom, including the type of quark. You cannot just apply it to each quark flavor individually.

This is the table of elementary particles, and if you read it carefully you will see that there are a number of quantum numbers, not only charge and mass, the make them individual and distinguishable.

Distinguishable fermions do not fall into the Pauli exclusion principle.

The proton is composite , and also in addition to charge has baryon number 1, the positron ( antiparticle of the electron ) has baryon number zero and lepton number 1, also their mass is very different. So they are distinguishable and do not obey the Pauli exclusion.

• They obey Pauli exclusion, it's just that Pauli exclusion doesn't prohibit the proton and electron from co-existing. Sep 27, 2018 at 18:00
• @Acccumulation maybe my engish is at fault. I though exclusion comes from exclude ,and that means that the state is excluded if it follows the principle. Sep 27, 2018 at 18:07
• When you have a rule "If A, then B", then in cases where A is false, the rule is being followed. For instance, if there's a rule that says that vehicles with more than two axles can't drive more than 55 mph, and you're driving a vehicle with two axles at 60 mph, you're not violating the rule. Sep 28, 2018 at 14:40

The Pauli Exclusion Principle is that no two indistinguishable fermions may occupy the same quantum state. It does not apply to pairs of distinguishable fermions (e.g. a neutron and a proton). If it did, then nuclear physics would be very different. See Are protons and neutrons affected by the Pauli Exclusion Principle?

Distinguishable fermions may be distinguished from each other by their mass, charge, spin, isopin etc.

• there’s some semantic distinction between identical and indistinguishable. In the case where fermions have different masses etc, they are not identical and thus cannot possibly be indistinguishable. Two fermions could be identical yet distinguishable if they were so far apart that their wavefunction would practically not overlap. Feb 2, 2023 at 20:50