Calculation of elements of spin groups using generalized Pauli's theorem

TL;DR

This paper generalizes Pauli's theorem for real and complex Clifford algebras, providing matrix analogues and an algorithm to compute spin group elements corresponding to orthogonal group elements.

Contribution

It introduces generalized theorems for Clifford algebras and develops an algorithm for calculating spin group elements from orthogonal group elements.

Findings

Generalized Pauli's theorems for Clifford algebras.

Matrix formalism analogues of these theorems.

An algorithm for computing spin group elements.

Abstract

We formulate generalizations of Pauli's theorem on the cases of real and complex Clifford algebras of even and odd dimensions. We give analogues of these theorems in matrix formalism. Using these theorems we present an algorithm for computing elements of spin groups that correspond to elements of orthogonal groups as double cover.