Talk:Fermion

So a grain of sand prevents another grain of sand from occupying the same location.

Unless it's cold enough to form a bose einstein condensate!

BECs are formed out of bosons! Hence "bose." However, fermions can form condensates -- but they are condensates in momentum space only, not physical space. (i.e., the condensate has lots of fermions with the same momentum, but they are not all in the same place), so the Pauli ex. principle is not violated.

Can you explain this or point to a reference? As far as I'm aware, there's no difference in this respect between position space and momentum space -- antisymmetry in both cases requires the wavefunction to vanish at equal position/equal momentum. Fpahl 06:15, 8 Oct 2004 (UTC)

---

The Pauli exclusion principle doesn't always work, according to my quantum textbook. See my discussion in talk:Pauli exclusion principle. -- Tim Starling

The result of that discussion was that the textbook meant not that it doesn't always work, but that in some circumstances it's a safe approximation to ignore it in calculations. Tim agreed, so I guess the comment above is just a leftover. Fpahl 06:15, 8 Oct 2004 (UTC)

---

I'm wondering whether the article's definition of fermions as particles requiring anti-symmetric states is the best approach. According to the spin-statistics theorem, this is equivalent with having half-integer spin. But if a particle were found to violate that theorem, say a particle with integer spin and anti-symmetric wavefunction (I'm aware that it's not clear how this could be and it would probably require a major change in quantum field theory), would we say "we found a fermion whose spin isn't half-integer", or would we say "we found a boson whose state isn't symmetric"? I think the latter, which would imply that the definition of a fermion is a particle with half-integer spin. This is also how Eric Weisstein's World of Physics (http://scienceworld.wolfram.com/physics/Fermion.html) defines it. (The same applies, obviously, to bosons; I added a link to this discussion on their talk page.) Fpahl 06:15, 8 Oct 2004 (UTC)

I disagree with you. For me, a fermion is an anti-commuting operator (in "second quantization" formalism) and an expression like "spinless fermion" is not self-contradictory. _R_ 14:54, 8 Oct 2004 (UTC)

You're right. A survey of my QFT textbooks yielded overwhelming evidence for this view, with two books explicitly stating the spin-statistics theorem as saying that fermions have half-integer spin, not that they anti-commute. I could be forgiven, though, since Kaku in "Quantum Field Theory: A Modern Introduction", one of the standard texts, writes: "To demonstrate the spin-statistics theorem, let us quantize bosons with anticommutators and arrive at a contradiction. ... Likewise, one can prove that fermions quantized with commutators violates microcausality." This only makes sense if "fermions" is taken to mean "particles with half-integer spin".

Do I understand correctly that in the above admittedly unlikely scenario you would be inclined to say "we found a fermion whose spin isn't half-integer"? Fpahl 15:24, 8 Oct 2004 (UTC)

Interestingly, our own article on the spin-statistics theorem takes the other view. Would you agree it should be changed accordingly? Fpahl 15:28, 8 Oct 2004 (UTC)

A new twist to the story: I emailed mathworld about this since your view suggests that their definitions are wrong, and they sent me this:

The Particle Data Group controls these definitions.  Here are the
definitions from Particle Data Group: 

Fermion: Any particle that has odd-half-integer (1/2, 3/2, ...)
intrinsic angular momentum (spin), measured in units of h-bar. All
particles are either fermions or bosons. Fermions obey a rule called the
Pauli Exclusion Principle, which states that no two fermions can exist
in the same state at the same time. Many of the properties of ordinary
matter arise because of this rule. Electrons, protons, and neutrons are
all fermions, as are all the fundamental matter particles, both quarks
and leptons.

Boson: A particle that has integer intrinsic angular momentum (spin)
measured in units of h-bar (spin =0, 1, 2, ...). All particles are
either fermions or bosons. The particles associated with all the
fundamental interactions (forces) and composite particles with even
numbers of fermion constituents (quarks) are bosons.

Has the Particle Data Group got it wrong?! Fpahl 17:07, 8 Oct 2004 (UTC)

I would argue that the PDG is primarily concerned with particle phenomenology, and thus intends their definition to discriminate solely between existing particles (for which the distinction between the definitions in question is moot). In QFT, it's certainly the case that when we say "fermion" we mean "fields represented by anticommuting Grassman numbers". If we want to talk about a particle that happens to have spin-1/2 but commutes, we'd call it a "pseudofermion". So one might argue that both characteristics are necessary for a particle to be a fermion, and thus that there are really four classes of particle: fermion, boson, pseudofermion and pseudoboson; only two of which actually exist. -- Xerxes 18:53, 2004 Oct 8 (UTC)

(Note: I wrote the following before seeing Xerxes' answer) Of course, it's got it wrong! What else do you expect from particle physicists? Seriously though, the flaw in this definition is the following: how do you count the number of fermion constituents in a phonon?

The more I think of it, the more I believe it depends on whether you focus on individual particles (in which case fermion=half-integer spin) or on their collective behaviour (in which case fermion=anticommuting operator=antisymmetric wavefunction). _R_ 19:05, 8 Oct 2004 (UTC)

Fermions with odd integer spin

We have all noticed that spin is described as being a multiple of hbar/2. I thought that it would be better to set this value to a constant giving,

hdot = hbar/2 = 5.2728584118222738157569629987­554e-35 J.s

But now the equations for spin did not work with hdot, so I had to correct them.

Here are the corrected equations,

|sv| = sqrt(s(s + 2)) * hdot

and

Sz = ms.hdot

where,

sv is the quantized spin vector,

|sv| is the norm of the spin vector,

s is the spin quantum number, which can be any non negative integer,

Sz is the spin z projection,

ms is the secondary spin quantum number, ranging from -s to +s in steps of two integers

For spin 1 particles this gives:

|sv| = sqrt(3).hdot and Sz = -hdot, +hdot

For spin 2 particles this gives:

|sv| = sqrt(8).hdot and Sz = -hdot, 0, +hdot

Now that the spin equations have been corrected, the definitions for fermions and bosons are incorrect, and must be redefined as follows.

Fermions are particles that that have an odd integer spin.

Bosons are particles that have an even integer spin.

Would these redefinitions have any other effects on the Standard Model?

Can these redefinitions explain any currently unexplained phenomena?

Are there any experiments that could confirm or refute these claims?

I would like eveyone to have a good think about this, and give me your objections to it, or even data to support it.

The change you're proposing is a trivial renormalization; physicists are perfectly happy with the convention as it stands, tho mathematicians studying lie groups tend to use a normalization with steps of two. -- Xerxes 17:47, 2005 Jun 8 (UTC)