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arXiv · 1607.08732

Mapping curved spacetimes into Dirac spinors

Carlos Sabín
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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.

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Carlos Sabín. 2016-07-29. Mapping curved spacetimes into Dirac spinors. https://doi.org/10.1038/srep40346

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