I am not so sure about that since this as far as I know was never confirmed by experiment. Theoretically, this could be tested on any fermion by experiment since neutrinos have a tiny intrinsic magnetic dipole moment so they can be rotated in the lab frame using Larmor precession under an external magnetic field but I don't believe a neutrino can ever be trapped to perform this type of experiment similar to neutron interferometry used for measuring the 4π-symmetry of electrons.

I think in your first sentence, you mean spinor, rather than tensor.

@Markoul11 Neutrino spin can be inferred experimentally from conservation of angular momentum in processes like beta decay.

@Andrew yes thank you.

@Markoul why do you expect neutrinos to be different than other fermions?

@Markoul11 I didn't assume that (although it is a result you can derive within relativistic quantum field theory called the spin-statistics theorem). As I said, you can confirm the neutrino spin experimentally if you assume conservation of angular momentum (which is a much weaker assumption than that neutrino spin is 1/2), and measure the angular momentum in a process like beta decay.

@Andrew he says that some half-spin*N integer particles(neutrinos) dont need to obey Fermi-Dirac statistics.Why would neutrinos be any different?They could(since we cant interact with them very much) but this would be really weird!Also I think your question simply has the answer:"We dont know ,because we havent looked at it yet."

Yes, maybe the 4π-symmetry for fermions breaks down in some case?

@Markoul11 see my previous post.I think most scientists "take for granted" that neutrinos obey Fermi-Dirac statistics.

I'm not going to keep commenting but no serious physicist doubts that fermions obey Fermi-Dirac statistics. As I've said above, this is both for good theoretical and experimental reasons. It's not something people just assume for no good reason. You could win a Nobel prize by showing this wasn't true so it's not like there isn't an incentive for scientists to buck the status quo; they believe it because there is very strong theoretical and experimental evidence that this is the case.

@Andrew this question should be a PhD , not being asked in a Q&A forum(because it is beasically research) but who cares?

I can see the theoretical reasons of why it is believed that neutrinos obey the so called Fermi-Dirac Statistics model but I have a difficulty to find experiment references? In any case neutrinos have proved to be strange particles with unique properties differentiating them from other SM particles like neutrino oscillations. It would no surprise me to find that they brake the 4π-symmetry.

@Markoul11 we simply dont know because we cant interact with many neutrinos but we are certain 99.9% because why would they be different?Nature avoids unnecessary complexities.To check up if neutrinos followed the Fermi-Dirac statistics , we would need to measure a beam of neutrinos and study its properties but because they interact very rarely with ordinary matter it is impossible to do that.

@Markoul11 what the classical analog of your question is to test if a 3-body system is deterministic,we simply cannot prove it but we are sure that it has to be this way because the 2-body system is well solved.

@Markoul11 also r u Greek(am wondering)?

@RootGroves I am currently doing theoretical work showing a possible correlation of neutrinos being found to be always left-handed with 4π-symmetry breaking,

@Markoul11 Hi!Could you link us in your work?I am really interested.Maybe not here my gmail is [email protected] you mind , please do send me your work or post another question.Btw I have to warn you that this site is Q&A so research is not considered "mainstream physics".

@Markoul11 I mean I would argue that we only find left-handed neutrinos because maybe neutrinos are Majorana particles so the weak interaction doesnt allow for right handed neutrinos , not sure tho.

@RootGroves quote: "...maybe neutrinos are Majorana particles?" It's the same question herein rephrased. IMO a Majorana fermion must have a 2π-symmetry similar to photons (Bosons)

@Markoul11 Nah Majorana fermions and bosons are a different thing, bosons are not Majorana fermions.