 the 3-dimensional space, and has nothing to do with any other arguments (in particular with experiment). This is purely theoretical argument. 
Qualitatively about the spin
The spin is the quantity whose importance fundamentally emerges because of the Poincare symmetry of our world. Apart from its physical sense, it is the quantum number by which we mathematically characterize each (at least massive) particle due to its transformation properties under the Poincare group. Through the representations of the Poincare group, the description of the spin is related to the topology of the space-time.
The relation between the spin and statistics
So where these two conceptions, the spin and the statistics, meet each other? How the spin affects the statistics (and vice versa) and, in particular, how the Pauli exclusion principle follows from this? From the first point of view any relation between them is unnatural, at least from the point of view of topology. However, actually the relation exists.
The poincare invariance of the quantum theory requires that the hamiltonian density $\hat{H}(x)$ of the theory must commute with itself for space-like intervals:
$$
\tag 2 [\hat{H}(x),\hat{H}(y)] = 0 \quad \text{for} \ (x-y)^2<0
$$ 
The hamiltonian is composed from the field operators $\hat{\psi}_{a}(x), \hat{\psi}_{b}(y)$ quantized in terms of creation-destruction operators $\hat{a}(\mathbf p, s),\hat{a}^{\dagger}(\mathbf p, s)$ of the particles with arbitrary spin $s$. From the relation $(1)$ we know that the creation-destruction operators must obey
$$
\tag 3 [\hat{a}(\mathbf p, s),\hat{a}(\mathbf k, s)]_{\pm} =0,\quad [\hat{a}(\mathbf p, s),\hat{a}^{\dagger}(\mathbf k, s)]_{\pm} \sim \delta(\mathbf p -\mathbf k)
$$
Note that this statement is purely theoretical and has nothing to do with the phenomenology. By taking into account both $(2),(3)$, we obtain that
$$
\tag 4 [\hat{\psi}_{a}(x),\hat{\psi}_{b}(y)]_{\pm} = 0, \quad (x-y)^{2} < 0
$$
The structure of the field operators are completely fixed by their
the 3 - dimensional space, and has nothing to do with any other argument (in especial with experiment). This is purely theoretical argument. 
 Qualitatively about the spin 
 The tailspin is the quantity whose importance fundamentally emerges because of the Poincare isotropy of our worldly concern. Apart from its forcible common sense, it is the quantum number by which we mathematically characterize each (at least massive) atom due to its transformation properties under the Poincare group. Through the representations of the Poincare group, the description of the tailspin is related to the topology of the space - time. 
 The relation between the spin and statistics 
 thus where these two conceptions, the spin and the statistics, touch each other? How the spin affects the statistic (and vice versa) and, in finical, how the Pauli exclusion principle follows from this? From the inaugural point of view any relation between them is unnatural, at least from the point of view of topology. However, actually the relation exists. 
 The poincare invariance of the quantum theory requires that the hamiltonian density $ \hat{H}(x)$ of the theory must commute with itself for space - like time interval: 
 $ $ 
 \tag 2 [ \hat{H}(x),\hat{H}(y) ] = 0 \quad \text{for } \ (x - y)^2<0 
 $ $ 
 The hamiltonian is composed from the sphere operators $ \hat{\psi}_{a}(x), \hat{\psi}_{b}(y)$ quantize in terms of creation - end operators $ \hat{a}(\mathbf p, s),\hat{a}^{\dagger}(\mathbf p, s)$ of the particle with arbitrary spin $ s$. From the relation $ (1)$ we acknowledge that the creation - destruction operators must obey 
 $ $ 
 \tag 3 [ \hat{a}(\mathbf p, s),\hat{a}(\mathbf k, s)]_{\pm } = 0,\quad [ \hat{a}(\mathbf p, s),\hat{a}^{\dagger}(\mathbf k, s)]_{\pm } \sim \delta(\mathbf p -\mathbf k) 
 $ $ 
 Note that this affirmation is purely theoretical and has nothing to do with the phenomenology. By taking into report both $ (2),(3)$, we receive that 
 $ $ 
 \tag 4 [ \hat{\psi}_{a}(x),\hat{\psi}_{b}(y)]_{\pm } = 0, \quad (x - y)^{2 } < 0 
 $ $ 
 The structure of the field operators are completely fixed by their
 thf 3-dimensional space, and mas nothing to do with eny othsr argumdnts (in particular with expecimebt). Thus is purely theoreticxl argumejt. 
Qualiratitely about the s'jn
The sinn is bhe qbaitity whose impprtance futdamentally emareed because of the Poincare symmetry jf our eogld. Apart from its [hysjbao sense, it is the quantum numger by xhich we mathemstically characterize each (at peast massive) partlcle due to its rransformatiun propertpzs under thg Poincare group. Through the repfesencations of jkw Plhncare grou', the qescription of the s[in is telated to the to'oloty of the space-time.
Thx relation between tre spin atd statistics
So wheee thesg two conzwptkona, vhe spin wnd the statiatics, meet wach other? How the xpyb affects the statiftycs (and vice versa) and, in particular, hof tge Pauli exclusion prinxiple follows from thls? From tre first point of view any relation between them hs uniagurco, at uwadt from the point of view of topology. However, zcuuakly the relatijn exists.
Thr ooogcare invariavce of ths quantum theory rfquires that the hamijtonoan density $\hat{H}(x)$ of the thwory must coinute with itself flr space-likz intetvals:
$$
\tsg 2 [\hat{H}(x),\hat{H}(y)] = 0 \quad \tzxt{for} \ (x-y)^2<0
$$ 
The haliltonian ks composed from thv fiald operators $\hat{\psi}_{a}(x), \hat{\[si}_{b}(y)$ quaitizeb in teros og creaeion-destruftion operators $\hat{a}(\mathhf p, d),\hdt{a}^{\dagger}(\mwthbf p, s)$ of the particles with arbitrary spim $v$. Fgom the rzlatiok $(1)$ we know that the creation-dgstructiou operxtors must obey
$$
\taj 3 [\hat{a}(\mathbs p, s),\hat{a}(\mathtv k, s)]_{\pm} =0,\quad [\hat{a}(\matrbf p, s),\hqt{a}^{\daggdf}(\mathbf k, s)]_{\pm} \xim \delta(\mathbf p -\mqthbf k)
$$
Note that tmis sjafement is purelv uhworetical and nas noehpng tj do with the phevomdmologh. By taking knto account both $(2),(3)$, we obdain that
$$
\tag 4 [\hat{\psi}_{a}(x),\nab{\psi}_{b}(y)]_{\pm} = 0, \quad (x-r)^{2} < 0
$$
The structire of the field okeratocs are compketgly fixed by their
the 3-dimensional space, and has nothing to any arguments (in with experiment). This about spin The spin the quantity whose fundamentally emerges because of the Poincare of our world. Apart from its physical sense, it is the quantum number which we mathematically characterize each (at least massive) particle due to its transformation under Poincare Through representations of the Poincare group, the description of the spin is related to the topology of space-time. The relation between the spin and statistics where these two conceptions, spin and the statistics, meet other? the spin the (and versa) and, in how the Pauli exclusion principle follows from this? From the first point of view any relation between is unnatural, from the of of However, actually the The poincare invariance of the quantum the hamiltonian density $\hat{H}(x)$ of the theory must with itself space-like intervals: $$ \tag 2 [\hat{H}(x),\hat{H}(y)] 0 \quad \text{for} \ (x-y)^2<0 $$ The hamiltonian composed from the field operators $\hat{\psi}_{a}(x), \hat{\psi}_{b}(y)$ quantized in terms of creation-destruction operators $\hat{a}(\mathbf p, s)$ of the particles arbitrary spin $s$. the $(1)$ know the creation-destruction must obey $$ \tag 3 [\hat{a}(\mathbf p, s),\hat{a}(\mathbf k, s)]_{\pm} =0,\quad p, s),\hat{a}^{\dagger}(\mathbf k, s)]_{\pm} \sim \delta(\mathbf p -\mathbf k) $$ this is purely theoretical has nothing to do the By taking into account we that [\hat{\psi}_{a}(x),\hat{\psi}_{b}(y)]_{\pm} 0, (x-y)^{2} < 0 $$ structure of the field operators completely fixed by their
 the 3-dimensional space, and has Nothing to dO with Any OthEr ArguMentS (in particular wITh exPeriment). This is purely thEoretIcAL argUMeNt. 
QuaLitativELy ABOut ThE sPin
thE SpIn is tHe qUantity Whose imporTanCe FundamentallY EmErges becauSe oF the Poincare SymMetry oF oUr wORld. ApArt From iTs physICal senSe, it is the QuANtum nuMBer by whICH wE matHematically characTErIZe each (at least mAssive) PaRTiCLE duE to Its transfoRmAtion PRopertiES uNDER thE poincare group. through the rEPreSentatIoNs oF The PoiNcare GrOUp, tHe descriptiOn of The spin is RelateD To the toPOlogy of The spaCe-tIme.
the rELaTiOn bEtWEen THe SpiN And StatistiCs
so Where ThesE TWO ConcEptIons, The spIn and the statiStiCs, meET eaCh othEr? How The sPiN affeCts the StatiStIcs (and vice versa) And, iN particulAr, hOw The paUli exCLusion PriNciPle follOws from THis? frOM THe First point of view anY rELAtIon betweEn them IS uNnATural, at lEaSt fRom tHE Point Of viEW oF topologY. HowevER, aCtUally thE rElatioN eXisTs.
THe poiNCare InvariAnce of thE quanTUm theory requirES that the hamilTOnIAN dENsitY $\haT{H}(x)$ of the theOry mUSt coMmutE WiTh iTSelf fOr spaCe-LIkE Intervals:
$$
\tag 2 [\hat{H}(x),\haT{H}(Y)] = 0 \quad \tExt{foR} \ (x-y)^2<0
$$ 
The hamiltoNian is compOSED from the FielD OpERators $\hat{\psi}_{a}(x), \Hat{\psI}_{b}(y)$ quantizED in terms Of creAtion-desTruction oPERators $\haT{a}(\mAthBf p, S),\haT{A}^{\DaGger}(\mathbf p, s)$ oF THe paRtIcles wiTh aRbitrarY spIn $s$. froM thE rElation $(1)$ we Know that ThE cReAtIon-DestrUCtion opeRaTorS mUst Obey
$$
\tAG 3 [\hat{a}(\mAthbf P, s),\haT{a}(\MaTHbf K, s)]_{\pm} =0,\quaD [\HaT{A}(\MathBf P, s),\Hat{a}^{\DagGeR}(\mathBf k, s)]_{\PM} \siM \delta(\mAthbf p -\matHbf K)
$$
note ThAt This staTement is purelY tHeoretical AnD haS nothiNG To do with The phenomenology. By takinG Into accOunT both $(2),(3)$, We obTain that
$$
\tAg 4 [\hAt{\psi}_{a}(X),\haT{\Psi}_{b}(y)]_{\pM} = 0, \quad (x-Y)^{2} < 0
$$
The sTrUctURE of thE FIeLd oPeRators are cOMPleTely fIxEd by Their
 the 3-dimensional space,and has no thing  to  do  w ithanyother argument s  (in  particular with exper iment ). This is  pure ly theo r et i c alar gu men t. 
Q ualit ati vely ab out the sp inTh e spin is th e  q uantity wh ose  importancefun dament al lye merge s b ecaus e of t h e Poin care symm et r y of o u r world . Ap artfrom its physical se n se, it is thequantu mn um b e r b y w hich we ma th emati c ally ch a ra c t e riz e  each (at lea st massive) par ticledu e t o  its t ransf or m ati on properti es u nder thePoinca r e group .  Throug h therep res enta t io ns  of  t h e P o in car e  gr oup, the  d es cript iono f t he s pin  isrelat ed to the top olo gy o f  th e spa ce-ti me.Th e rel ationbetwe en  the spin and s tati stics
Sowhe re  th es e two concep tio ns,  the sp in andt hest a t i st ics, meet each oth er ? Ho w the sp in aff e ct st he stati st ics  (an d vicevers a )and, inpartic u la r,  how th ePauliex clu sio n pri n cipl e foll ows from  this ?  From the firs t  point of vie w  a n y  r e lati onbetween the m is unna tura l ,atl eastfromth e  p o int of view of topo lo gy. Ho wever , actually th e relation e x ists.
Th e po i nc a re invarianceof th e quantumt heory re quire s that t he hamilt o n ian dens ity  $\ hat {H} ( x )$  of the theor y must  c ommutewit h itsel f f orspa ce- li ke interv als:
$$\t ag  2  [ \ha t{H}( x ),\hat{H }( y)]  =  0\quad \text{ for}\ (x -y )^ 2 <0$$ 
The ha m i lton ia nis c omp os ed fr om t h e f ield op erators $ \ha t {\ps i} _{ a}(x),\hat{\psi}_{b }( y)$ quanti ze d i n term s of creat ion-destruction operato r s $\hat {a} (\mat hbfp, s),\ha t{a }^{\da gge r }(\mat hbf p,  s)$of  th e parti c l es  wi th  arbitrary s pin  $s$.  F romthe rel ation $(1)$ we kno w  th at the creati on- dest r u ct ion op e rat or s  mu s t  obey
$$
\tag 3  [\hat{a}( \m a th bf p, s),\ h at{ a} (\mathb f k, s) ]_{\p m } =0,\q uad [\hat {a}(\math bf  p,s ) ,\h at{a}^{\da gger}(\m athbf k,s )]_{\ p m}  \sim  \d elta(\ ma thb f p - \mathb f  k) 
$$
N ote th at  thisstate me nt is pu rely theoretical and ha s noth ing t o d o with th e p h eno menology.  Bytaking int o a cco unt b oth $(2), (3)$ ,  w e o b tainthat $$
\tag 4 [\ hat { \ ps i}_{a}(x),\ h a t {\p si}_{ b}( y )]_{\p m} =  0, \quad (x-y)^{ 2 } < 0
$$
The s truc t u reoft he f ie ld operators a reco m p letely f ix ed by their 
 the_3-dimensional space,_and has nothing to_do with_any_other arguments_(in_particular with experiment)._This is purely_theoretical argument. 
Qualitatively about_the spin
The spin_is_the quantity whose importance fundamentally emerges because of the Poincare symmetry of our world._Apart_from its_physical_sense,_it is the quantum number_by which we mathematically characterize_each (at_least massive) particle due to its transformation properties_under_the Poincare group._Through the representations of the Poincare group, the description_of the spin is related to_the topology of_the_space-time.
The_relation between the spin_and statistics
So where these two conceptions,_the spin and the statistics, meet_each other? How the spin affects the_statistics (and vice versa) and, in_particular, how the Pauli exclusion_principle follows_from this? From the first_point of view_any relation_between them is_unnatural, at least from the point_of view of_topology. However, actually the relation exists.
The_poincare_invariance of the_quantum_theory_requires that_the hamiltonian density_$\hat{H}(x)$_of the_theory_must commute with itself for space-like_intervals:
$$
\tag_2 [\hat{H}(x),\hat{H}(y)] = 0 \quad \text{for} \_(x-y)^2<0
$$ 
The hamiltonian is_composed_from the field operators_$\hat{\psi}_{a}(x), \hat{\psi}_{b}(y)$ quantized in terms_of creation-destruction operators $\hat{a}(\mathbf p, s),\hat{a}^{\dagger}(\mathbf_p, s)$_of the_particles with arbitrary spin $s$. From the relation $(1)$ we know_that the creation-destruction operators must obey
$$
\tag_3 [\hat{a}(\mathbf p, s),\hat{a}(\mathbf_k, s)]_{\pm}_=0,\quad_[\hat{a}(\mathbf p, s),\hat{a}^{\dagger}(\mathbf_k,_s)]_{\pm} \sim_\delta(\mathbf p -\mathbf k)
$$
Note that this statement_is purely_theoretical and has nothing to do_with the phenomenology. By_taking_into account both $(2),(3)$, we obtain_that
$$
\tag 4 [\hat{\psi}_{a}(x),\hat{\psi}_{b}(y)]_{\pm} = 0, \quad_(x-y)^{2} < 0
$$
The structure of_the_field_operators are completely fixed by_their