Introduction to supersymmetric spin networks

TL;DR

This paper introduces supersymmetric spin networks, exploring their mathematical structure and potential applications in quantum supergravity and gauge theories, with a focus on the superalgebra $Osp(1|2n)$.

Contribution

It provides a comprehensive introduction to supersymmetric spin networks and demonstrates their basis properties in the associated Hilbert space, including the q-deformed case.

Findings

Spin network states form an orthogonal basis of the Hilbert space.

The construction applies to both classical and q-deformed cases.

Potential applications in quantum supergravity and gauge theories.

Abstract

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 $Osp(1|2n)$. It turns out that the set of corresponding spin network states forms an orthogonal basis of the Hilbert space $\cal L\mit^2(\cal A\mit/\cal G)$, and this argument holds even in the q-deformed case. The $Osp(n|2)$ 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.