
TL;DR
This paper derives an exact Green function for fermions on a manifold with non-trivial topology, revealing connections between topology, particle statistics, and potential mass generation in higher dimensions.
Contribution
It provides a novel exact expression for the fermionic Green function on manifolds with non-trivial topology, linking topology to particle statistics and mass generation mechanisms.
Findings
Exact Green function expression for fermions on $ e imes orus^{D-1}$
Topological measures related to particle statistics in 2D and 3D
Potential implications for mass generation in higher dimensions
Abstract
An exact expression for the Green function of a purely fermionic system moving on the manifold , where is a -torus, is found. This expression involves the bosonic analog of corresponding to the irreducible representation for the n-th class of homotopy and in the fermionic case for D=2 and 3, is a measure of the statistics of the particles. For higher dimensions (), 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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