Geometric Classification of Topological Quantum Phases

TL;DR

This paper introduces a geometric model linking topological quantum phases to elements of transformation groups, based on scattering around space-time defects in higher dimensions, offering a new perspective on quantum phase classification.

Contribution

It presents a novel geometric framework for classifying topological quantum phases using transformation groups and space-time defect scattering.

Findings

Establishes a correspondence between quantum phases and transformation group elements

Provides a geometric interpretation of topological phase emergence

Suggests a unified approach to classify phases via higher-dimensional scattering

Abstract

On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a transformation group.