Mapping curved spacetimes into Dirac spinors

TL;DR

This paper presents a method to map solutions of the Dirac equation in flat spacetime to curved spacetime using local phase transformations, enabling quantum simulations of Dirac particles in curved backgrounds.

Contribution

It introduces a technique to encode curved spacetime effects into flat spacetime Dirac equations through phase transformations, facilitating quantum simulation of curved spacetime physics.

Findings

Solutions in curved spacetime can be obtained from flat spacetime solutions via phase transformations.

The method allows existing quantum simulators to incorporate effects of curved spacetime.

Applied to specific 1+1 dimensional spacetimes, demonstrating practical utility.

Abstract

We show how to transform a Dirac equation in curved spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1+1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1+1 dimensions.