离散量子引力与量子场论
Discrete Quantum Gravity and Quantum Field Theory
摘要：
我们引入一个离散的4维模的整数，似乎有极大的对称性。通过邻接通常的Minkowski距离，我们得到一个离散的4维Minkowski空间。在这个空间中形成宇宙历史，并采用标准因果顺序，历史成为因果集。这些因果集的大小迅速增加，并描述了早期宇宙的暴胀时期。接下来我们考虑模的对称群$G$。证明了$G$的阶为24，并构造了它的群表.在某种意义上，$G$是洛伦兹群的离散近似。然而，我们注意到它不包含提升，本质上是一个旋转群。构造了$G$的酉表示。得到了与离散模对偶的能量-动量空间，并导出了一个量子形式。在此结构上引入离散的Fock空间，并考虑自由量子场.最后，我们在相互作用量子场的研究中迈出了第一步。
英文摘要：
We introduce a discrete 4-dimensional module over the integers that appears to have maximal symmetry. By adjoining the usual Minkowski distance, we obtain a discrete 4-dimensional Minkowski space. Forming universe histories in this space and employing the standard causal order, the histories become causal sets. These causal sets increase in size rapidly and describe an inflationary period for the early universe. We next consider the symmetry group $G$ for the module. We show that $G$ has order 24 and we construct its group table. In a sense $G$ is a discrete approximation to the Lorentz group. However, we note that it contains no boosts and is essentially a rotation group. Unitary representations of $G$ are constructed. The energy-momentum space dual to the discrete module is obtained and a quantum formalism is derived. A discrete Fock space is introduced on this structure and free quantum fields are considered. Finally, we take the first step in a study of interacting quantum fields.
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