Braid statistics

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical physics</a>, braid statistics is a generalization of the <a href="/facts/Spin%25E2%2580%2593statistics_theorem/j2qqVpez">spin statistics</a> of <a href="/facts/Boson/XtPFcjb5">bosons</a> and <a href="/facts/Fermion/LEckdDsR">fermions</a> based on the concept of <a href="/facts/Braid_group/rn5323Kx">braid group</a>. While for fermions (bosons) the corresponding statistics is associated to a phase gain of 
  
    
      
        π
      
    
    {\displaystyle \pi }
  
 (
  
    
      
        2
        π
      
    
    {\displaystyle 2\pi }
  
) under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of 
  
    
      
        π
      
    
    {\displaystyle \pi }
  
 under such exchange  or even a non-trivial unitary transformation in the Hilbert space (see <a href="/facts/Anyon/hfgpCFjf">non-Abelian anyons</a>). A similar notion exists using a <a href="/facts/Loop_braid_group/wd7jxDt1">loop braid group</a>.
</p>

Braid statistics open-in-new

Braid statistics