标题： 引言：费米子的维度约化 显示英文标题

标题： Introduction to dimensional reduction of fermions

摘要： 我们提供了一个关于维度约化协议（DRP）的全面教学介绍，这是一个用于分析相互作用费米系统的不稳定性和临界点的多功能框架。 DRP 通过系统地降低有效空间维数同时保留关键物理特性，简化了多体问题的研究。 此方法适用于电子气体在各种环境下的研究：无论是在任意空间维度中，还是在存在泽曼场、自旋-轨道耦合作用的情况下，包括排斥或吸引相互作用。 专注于两点关联函数，DRP 确定一个与捕捉解析性质相关的最小子空间，促进了电子系统中临界现象的有效计算。 本文概述了 DRP 的假设、证明及其应用，强调其简单性和广泛适用性，为未来相关电子物理研究提供了方向。 显示英文摘要

摘要： We present a comprehensive pedagogical introduction to the dimensional reduction protocol (DRP), a versatile framework for analyzing instabilities and critical points in interacting fermionic systems. The DRP simplifies the study of many-body problems by systematically reducing their effective spatial dimension while retaining essential physics. This method works for electron gases in a diverse array of settings: in any number of spatial dimensions, in the presence of Zeeman fields, with spin-orbit coupling, including repulsive or attractive interactions. Focusing on two-point correlation functions, the DRP identifies a minimal subspace relevant for capturing analytic properties, facilitating efficient computation of critical phenomena in electronic systems. This work outlines the assumptions, proof, and applications of the DRP, emphasizing its simplicity and broad applicability for future studies in correlated electron physics.