Introduction to supersymmetric spin networks

In this paper we give a general introduction to supersymmetric spin networks. Its construction has a direct interpretation in context of the representation theory of the superalgebra. In particular we analyze a special kind of spin networks with superalgebra $Osp(1\mathrm{\mid }2n)$. It turns out that the set of corresponding spin network states forms an orthogonal basis of the Hilbert space $\mathcal{L}{\mathcal{\text{mit}}}^{\mathcal{2}}(\mathcal{A}\mathcal{\text{mit}}\mathcal{/}\mathcal{G})$, and this argument holds even in the q-deformed case. The $Osp(n\mathrm{\mid }2)$ spin networks are also discussed briefly. We expect they could provide useful techniques to quantum supergravity and gauge field theories from the point of non-perturbative view.