论文标题
细胞自动机在四个维度
Cellular automaton for spinor gravity in four dimensions
论文作者
论文摘要
某些费米子量子场理论等于概率的细胞自动机，而费米子占用数量与位相关。我们构造一个自动机，该自动机代表四个维度的旋转重力模型。局部洛伦兹对称性在离散水平上精确，而差异形态对称性在天真的连续性极限下出现。如果在真实的连续性极限中实现了差异对称性，我们的设置可以用作量子重力的模型，并在Vierbein的真实连续性极限和合适的集体磁场中实现，并获得了vierbein的合适集体和指标。对这个有趣的特定模型的讨论揭示了概率性细胞自动机的连续性极限的关键定性特征。如果概率信息足够光滑，则该限制可为大量单元提供。它与粗晶片有关。每个位配置在每个离散的时间步骤中都会更新到确切的一个新位配置的自动机属性不再在粗粒度级别上保持。职业数字的粗粒子配置可以演变为具有某些概率的许多不同的配置。量子场理论的这种特征可以随着连续时空对称性的出现而出现。
Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four dimensions. Local Lorentz symmetry is exact on the discrete level and diffeomorphism symmetry emerges in the naive continuum limit. Our setting could serve as a model for quantum gravity if diffeomorphism symmetry is realized in the true continuum limit and suitable collective fields for vierbein and metric acquire nonvanishing expectation values. The discussion of this interesting specific model reveals may key qualitative features of the continuum limit for probabilistic cellular automata. This limit obtains for a very large number of cells if the probabilistic information is sufficiently smooth. It is associated to coarse graining. The automaton property that every bit configuration is updated at every discrete time step to precisely one new bit configuration does no longer hold on the coarse grained level. A coarse grained configuration of occupation numbers can evolve into many different configurations with certain probabilities. This characteristic feature of quantum field theories can come along with the emergence of continuous space-time symmetries.
