Instituto de Física Fundamental, CSIC, Serrano, 113-bis, 28006 Madrid (Spain).
Sci Rep. 2017 Jan 11;7:40346. doi: 10.1038/srep40346.
We show how to transform a Dirac equation in a curved static 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 static 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 static 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.
我们展示了如何将弯曲静态时空中的狄拉克方程转换为平坦时空中的狄拉克方程。具体来说，我们表明，在一维平坦时空中自由无质量狄拉克方程的任何解都可以通过局部相位变换转换为相应的弯曲静态背景下的狄拉克方程的解，其中时空度规被编码到相位中。通过这种方式，现有的狄拉克方程量子模拟器可以自然地包含弯曲静态时空。作为第一个例子，我们使用我们的技术在一维中的一类有趣的时空中获得狄拉克方程的解。
