具有连续极限的1+1- QED的离散相对论时空形式
A discrete relativistic spacetime formalism for 1+1-QED with continuum limits
摘要：
我们构造了一个量子元胞自动机（QCA），它在已知的连续极限上与1+1 QED相一致。它包含在一个由幺正门组成的电路中，这个电路驱动一维晶格上粒子的演化，并使它们与链接上的规范场相互作用。粒子是大质量的费米子，演化完全是U（1）规范不变的。我们证明了，在连续时间离散空间极限，QCA收敛到Kogut-Susskind交错版本的1+1 QED。我们还表明，在连续的时空限制和在自由的一个粒子部门，它收敛到狄拉克方程，一个强有力的迹象表明，该模型仍然是准确的相对论制度。
英文摘要：
We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut-Susskind staggered version of 1+1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation, a strong indication that the model remains accurate in the relativistic regime.
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