论文标题
从三个空间维度中的量子细胞自动机的费米子和玻色量量子场理论
Fermionic and bosonic quantum field theories from quantum cellular automata in three spatial dimensions
论文作者
论文摘要
在晶格上的量子行走可能会导致长波长极限的相对论波方程，但是超越单粒子的情况已被证明具有挑战性，尤其是在一个以上的空间维度中。我们基于两个不同的量子步道来构建可区分颗粒的量子细胞自动机，并表明，可以分别限制对反对称和对称子空间，可以产生三个空间维度中的自由费米子和玻色子的多颗粒理论。这种构建逃避了一种无关的定理，该定理禁止在一个以上的空间维度中使用通常的效费结构。在长波长限制中，这些恢复了狄拉克场理论和麦克斯韦场理论，即自由QED。
Quantum walks on lattices can give rise to relativistic wave equations in the long-wavelength limit, but going beyond the single-particle case has proven challenging, especially in more than one spatial dimension. We construct quantum cellular automata for distinguishable particles based on two different quantum walks, and show that by restricting to the antisymmetric and symmetric subspaces, respectively, a multiparticle theory for free fermions and bosons in three spatial dimensions can be produced. This construction evades a no-go theorem that prohibits the usual fermionization constructions in more than one spatial dimension. In the long-wavelength limit, these recover Dirac field theory and Maxwell field theory, i.e., free QED.
