Why in nature there is no spinless fermion?

[wdlang]

why?

i can see the link between spin value and the statistics in quantum mechanics

 

[Avodyne]

http://en.wikipedia.org/wiki/Spin-statistics_theorem

 

[fermi]

why?

i can see the link between spin value and the statistics in quantum mechanics

Well, actually there are spinless fermions of sorts. It just depends on what you define to be a "real" particle is. I am of course talking about Faddeev-Popov Ghosts in quantized non-Abelian Gauge theories. These particles are spinless fermions (in other words spin = 0, but they anti-commute.) However they do not possesses positive definite norm, which makes them less "real" if you like. More to the point, however, they depend on the choice of gauge. Interestingly, infinite renormalization constants depend on these spinless fermions, but finite gauge invariant quantities do not: they simply cancel out. This amazing fact is far from obvious by any argument that I have heard of. It takes a lot of hard formalism to prove it. So you decide for yourself if Faddeev-Popov Ghosts are real spinless fermions. Most physicists will not elevate them to the status of being "real" particles however.

 

[wdlang]

Well, actually there are spinless fermions of sorts. It just depends on what you define to be a "real" particle is. I am of course talking about Faddeev-Popov Ghosts in quantized non-Abelian Gauge theories. These particles are spinless fermions (in other words spin = 0, but they anti-commute.) However they do not possesses positive definite norm, which makes them less "real" if you like. More to the point, however, they depend on the choice of gauge. Interestingly, infinite renormalization constants depend on these spinless fermions, but finite gauge invariant quantities do not: they simply cancel out. This amazing fact is far from obvious by any argument that I have heard of. It takes a lot of hard formalism to prove it. So you decide for yourself if Faddeev-Popov Ghosts are real spinless fermions. Most physicists will not elevate them to the status of being "real" particles however.

i am not familiar with quantum field theory

i work in the low energy regime

the problem i am concerned with is, possibly there is no contradiction if we take a spinless or spin integer particle and impose fermionic commutation relations on it

 

[tom.stoer]

Which kind of expression do you have in mind?

If you do point-particle quantum mechanics then you should study something like Grassmann numbers (like in supersymmetric QM).

But in many cases there are not even commutation relations b/c the particles are not the canonical variables.Think about the non-rel. Pauli equation: I think you can plug in any spin you like. The fundamental variables are still x and p, so no anticommutation at all.

I think w/o using some sort of field theory you will never observe something like commutation or anticommutation relations between particles.

 

[saaskis]

the problem i am concerned with is, possibly there is no contradiction if we take a spinless or spin integer particle and impose fermionic commutation relations on it

If you are worried about the standard phrase "let us study spinless fermions" that you can find in many books on QM and condensed matter, then my answer would be no, there is no contradiction in imposing anticommutation relations on spinless fermions. Very often in non-interacting problems the spin degree of freedom is irrelevant, so you can forget it altogether and then, in the end, multiply your end result by a factor of two. In this case you just have too identical "flavors" of fermions that do not talk to each other. For example, most textbook solutions for the famous Tomonaga-Luttinger model (fermions in one spatial dimension) are done for spinless fermions, since then bosonization leads to a simple solution in terms of charge waves.

Things are of course very different for interacting systems, since the two spin species interact via Coulomb interaction. In the Tomonaga-Luttinger model, this leads to spin density waves that make matters a little bit more complicated.
EDIT: small clarification