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The spin-statistics connection, the Gauss-Bonnet theorem and the Hausdorff dimension of the quantum paths

Wellington da Cruz
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Abstract

We obtain an explicit expression relating the writhing number, $W[C]$, of the quantum path, $C$, with any value of spin, $s$, of the particle which sweeps out that closed curve. We consider a fractal approach to the fractional spin particles and, in this way, we make clear a deeper connection between the Gauss-Bonnet theorem with the spin-statistics relation via the concept of Hausdorff dimension, $h$, associated to the fractal quantum curves of the particles: \frac{h}{2+2s}=W[C]=\frac{1}{4π}\oint_{C}d x_α\oint_{C}d x_β ε^{αβγ} \frac{(x-y)_γ}{|x-y|^3}.

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Wellington da Cruz. 2004-02-26. The spin-statistics connection, the Gauss-Bonnet theorem and the Hausdorff dimension of the quantum paths. https://arxiv.org/abs/hep-th/0402131

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