Statistics and spin on two-dimensional surfaces

Balachandran, A. P. ; Einarsson, T. ; Govindarajan, T. R. ; Ramachandran, R. (1991) Statistics and spin on two-dimensional surfaces Modern Physics Letters A, 6 (30). pp. 2801-2810. ISSN 0217-7323

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The fundamental groups of the configuration spaces for the O(3) nonlinear σ-model on the compact genus g surfaces T2g and on the connected sums R2#T2g are known for any soliton number N. So are the braid for N spinless particles on these manifolds. The representations of these groups govern the possible statistics of solitons and particles. We show that when spin and creation/annihilation processes are introduced, the fundamental groups for the particles are the same as the corresponding σ-model groups. These fundamental groups incorporate the spin-statistics connection and are of greater physical relevance than the standard braid groups.

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