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arXiv · hep-th/9906100

Fermions on Non-Trivial Topologies

J. Gamboa
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Abstract

An exact expression for the Green function of a purely fermionic system moving on the manifold $\Re \times Σ^{D-1}$, where $Σ^{D-1}$ is a $(D-1)$-torus, is found. This expression involves the bosonic analog of $χ_n = e^{inθ}$ corresponding to the irreducible representation for the n-th class of homotopy and in the fermionic case for D=2 and 3, $χ_n$ 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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J. Gamboa. 2000-02-28. Fermions on Non-Trivial Topologies. https://doi.org/10.1016/s0370-2693(00)00243-4

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