Mapping curved spacetimes into Dirac spinors

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.

4 pages, 1 fig. v2: minor changes, published version

References in corpus (4)

• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Quantum simulation of the Klein paradox with trapped ions
• Klein tunneling and Dirac potentials in trapped ions
• Encoding relativistic potential dynamics into free evolution