From topological quantum mechanics to the physics of spin-one particles

TL;DR

This paper explores a topological quantum theory linking supersymmetric spin-one particles to topological sigma models, providing insights into particle behavior in curved spacetime, exemplified by gravitational effects near black holes.

Contribution

It introduces a novel topological framework for spin-one particles in curved spacetime, connecting supersymmetry with topological sigma models and demonstrating practical gravitational effects.

Findings

Established the equivalence between supersymmetric Lagrangian and topological sigma model.

Calculated the gravitational Stern-Gerlach effect for spin-one particles.

Extended the topological theory to curved spacetime environments.

Abstract

We give an example of topological theory whose Hilbert space contains physical objects: the N=2 supersymmetric Lagrangian of spin-one particles moving in D-dimensional space-time equals the Lagrangian of a topological sigma model in a (D+2)-dimensional target. The equivalence is valid for a curved space-time. As an application, we calculate the deviation of spin-one particles in a Schwarzschild background (gravitational Stern-Gerlach effect).