Fermions on Non-Trivial Topologies

Details Fermions on Non-Trivial Topologies Fermions on Non-Trivial Topologies

1999-06-14

arxiv.org/abs/hep-th/9906100v2

Phys.Lett. B477 (2000) 469-473

Physics

High Energy Physics

High Energy Physics - Theory

Some portions re-written, references added. To appear in PLB

Scientific paper

10.1016/S0370-2693(00)00243-4

An exact expression for the Green function of a purely fermionic system moving on the manifold $\Re \times \Sigma^{D-1}$, where $\Sigma^{D-1}$ is a $(D-1)$-torus, is found. This expression involves the bosonic analog of $\chi_n = e^{in\theta}$ corresponding to the irreducible representation for the n-th class of homotopy and in the fermionic case for D=2 and 3, $\chi_n$ is a measure of the statistics of the particles. For higher dimensions ($D \geq 4$), there is no analogue interpretation however this could, presumably, indicate a generation of mass as in quantum field theories at finite temperature.

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