The relevance of the Pauli group in dynamical systems with pseudo-fermions

Bavuma, Yanga

The relevance of the Pauli group in dynamical systems with pseudo-fermions

Doctoral Thesis

2021

Abstract

The group of Wolfgang Pauli is well known in mathematical physics, because it describes some relevant symmetries in quantum dynamical systems. It is less known its structure of finite 2-group of order 16, which may be decomposed in the central product of two of its subgroups. From this perspective, the Pauli group has an interesting structure at an algebraic level as well. Here a topological perspective is added to the literature. It is described the Pauli group as an appropriate quotient of the fundamental group of 3-dimensional Riemannian surfaces constructed as two distinct orbit spaces of the 3-dimensional sphere S3 ; one orbit space comes from the free action of the quaternion group Q8 on S3 ; another orbit space comes from a similar action of the cyclic group Z(4) of order 4 on S3. Applications are illustrated for Pseudo-fermionic operators, introducing a relevant framework of quantum mechanics. This suggests a physical interpretation for the topological decomposition, which has been found at an abstract level.

Keywords

Mathematics and Applied Mathematics

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PhD / Doctoral

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