标题： 算子维度分数量化 显示英文标题

标题： Operator Dimension Parity Fractionalization

摘要： 具有四维时空（4D）费米子的洛伦兹不变量子场论（QFT）在存在算符维度均为偶数的算符基的情况下具有$\mathbb{Z}_4$对称性，包括那些具有$d$的算符，以及那些具有$d > 4$的算符。 $\mathbb{Z}_4$对称性是算符维度奇偶性通过费米子数奇偶性扩展而来。 如果$\mathbb{Z}_4$无反常，这类QFT可以与三维拓扑超导体相关联。 此外，在标准模型有效场论中施加$\mathbb{Z}_4$对称性会严重限制违反重子数和轻子数的过程。 显示英文摘要

摘要： Lorentz invariant quantum field theories (QFTs) with fermions in four spacetime dimensions (4D) have a $\mathbb{Z}_4$ symmetry provided there exists a basis of operators in the QFT where all operators have even operator dimension, $d$, including those with $d > 4$. The $\mathbb{Z}_4$ symmetry is the extension of operator dimension parity by fermion number parity. If the $\mathbb{Z}_4$ is anomaly-free, such QFTs can be related to 3D topological superconductors. Additionally, imposing the $\mathbb{Z}_4$ symmetry on the Standard Model effective field theory severely restricts the allowed processes that violate baryon and lepton numbers.