Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

As a starting quantum physicist I am very interested in reasons why does Pauli's Exclusion Principle works. I mean standard explanations are not quite satisfying. Of course we can say that is because of fermionic nature of electrons - but it is just the different way to say the same thing. We can say that we need to antisymmetrize the quantum wavefunction for many electrons - well, another different way to say the same. We can say that it is because spin 1/2 of electron - but the hell, fermions has by the definition half-integral spin so it doesn't explain anything. Is the Exclusion Principle something deeper, for example in Dirac's Equation, like spin of the electron? I think it would be satisfying.

share|cite|improve this question

I think that while these "explanations" are all dancing around the same pole, they aren't created equal. I think the meat is in the fact that nature has a local Lorentz symmetry, so we expect to be able to decompose things into representations of the group $SO(3,1)$. It's a mathematical fact that this group (or it's algebra, rather) has integer and half-integer representations.

Once you have this structure, then a few meagre assumptions about causality and unitarity lead to the Spin-statistics theorem. In order to understand the proof you'll need to first dig deeper into the representations of the Lorentz group, and how they label single-particle states.

share|cite|improve this answer
@CheshireCat Perhaps add that the last step is that the spin-statistics theorem shows that for half integer spin representations the quantum state for two particles with quantum numbers $\vec{x}$ and $\vec{y}$ (I include "position" in the quantum number vector) is antisymmetric wrt swap of arguments $\psi(\vec{x}, \vec{y}) = -\psi(\vec{x}, \vec{y})$ so that now if two particles have the same quantum numbers $\psi(\vec{x}, \vec{x}) = - \psi(\vec{x}, \vec{x})$. A further piece of trivia which I like to dwell on here: when we represent the algebra by half integer representations, we're ... – WetSavannaAnimal aka Rod Vance Dec 30 '13 at 11:15
...actually representing the double cover $PSL(2,\mathbb{C})$ of the Lorentz group $SO(3,1)$, so you could say, with a slight strech, that the Dirac belt trick "proves" there are only bosons and fermions in the world. – WetSavannaAnimal aka Rod Vance Dec 30 '13 at 11:18

It's an observed phenomenon, aka a "Law of Nature." You can't prove it, but you can show that the underlying math & "description" of the particle's behaviour is consistent with this law.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.