Topological Symmetries

TL;DR

This paper introduces topological symmetries in quantum mechanics, revealing their algebraic structures and deriving supersymmetry and parasupersymmetry algebras through topological invariants.

Contribution

It defines topological symmetries involving topological invariants and derives their algebraic structures, connecting them to supersymmetry and parasupersymmetry.

Findings

Derived algebraic structures of topological symmetries

Connected topological symmetries to supersymmetry

Provided a novel derivation of supersymmetry algebras

Abstract

We introduce the notion of a topological symmetry as a quantum mechanical symmetry involving a certain topological invariant. We obtain the underlying algebraic structure of the Z_2-graded uniform topological symmetries of type (1,1) and (2,1). This leads to a novel derivation of the algebras of supersymmetry and $p=2$ parasupersummetry.