* Necessary Background :* Basics of quantum statistics(bosons fermions and all that) , a bit of topology(basically knowing what the word homotopy means)and some geometric imagination.

* Link :* from http://www.umsl.edu/~fraundor/p231/spinexcl.html

## half-integral spins and Pauli exclusion

**
Comment : ** It is a kind of popular science explanation on why fermions obey Pauli’s principle

**Posted By : ** Loganayagam.R.(Tom)

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though I am not totally sure of my own opinion, the refutation of such arguments as a proof for `spin-statistics connection’in an AJP article by Sudarshan and Duck sounds convincing:

Toward an understanding of the spin-statistics theorem by Ian Duck

and E. C. G. Sudarshan – Am J. Phys. V 66, pp 284.(Should be accessible inside IITK)

(Look under the section B3 `Topological markers and Feynman’s models’).

Interestingly, the argument is reminiscent (exactly same?) of the proof that a composite particle consisting of a fermion and a bosonic vortex in 2-d would be a boson (against the common intuition that boson+fermion= fermion). Basically, for exchanging the two composites you first rotate one around the other (without worrying about their internal structure) by 180 deg. which gives you a phase factor = -1 due to fermion. But since the composite has an internal structure you need to move the fermion around the vortex by 180 degree for truly exchanging the two composites. This gives an additional factor of -1, hence overall there is no sign change.

Hi Tarun,

I’m at home now and that means No AJP access for me for the next two months 😦 So, I would be able to read this article only if somebody can mail it to me…

And I don’t know much about the 2-d fermion-boson vortex – any references ? (Preferably from arXiv) I just wanted to confirm whether I understand this right – You start with a Fermionic+Bosonic field in 2+1 d (with Yukawa-type interactions ? ) and you find a vortex solution which has an extra topological phase which means that the actual spin of the composite particle is bosonic. If this is the way it is, it is way too cool . 🙂

And this reminds me of one another place where such naive intuitions about what can be a composite of what and what turn out to be wrong again due to a Toplogical phase. In case of Skyrme model( See for example Rational Maps, Monopoles and Skyrmions by Conor Houghton, Nicholas Manton, Paul Sutcliffe ), We can have fermions which come out as composites in a purely bosonic theory !

Now, coming back to the spin-statistics connection, What exactly is Sudarshan’s argument ? Is it that there might be other interesting topologogical phases prowling around and that they should be taken care of before we jump from odd under rotation to odd under exchange ?

Anyway, the comment is already long enough and I shall rather wait till I get hold of Sudarshan’s AJP article.

P.S.: I added a link to the AJP article from your comment. Hope you don’t mind..

hi there guys . i ‘ve got this great confusion abt 1/2 integral and integral spins of particles what actually is it . i read in some bokks . it is written that when this particles spin once they look same and some after 2 spins .

wht r they considering this particles as strings or spherical . u gotta help me with this ..

please