标题： 在二维欧几里得空间中关联电动力学和引力 显示英文标题

标题： Relating electrodynamics and gravity in two Euclidean dimensions

摘要： 二维电动力学与狄拉克费米子耦合，在一阶形式中被映射到二维引力，也包括费米子。 然而，由此产生的费米子-引力耦合偏离了传统形式，明确地破坏了宇称和时间反演对称性。 此外，这些费米子在$SO(2)$变换下表现出非传统的变换行为。 此外，我们使用路径积分形式和贝奇-鲁埃特-斯托拉-图廷技术，在量子层面上分析了这种映射的一致性。 我们的研究结果表明，量子电动力学和量子引力在量子层面上仍然等价。 显示英文摘要

摘要： Two-dimensional electrodynamics coupled to Dirac fermions is mapped onto two-dimensional gravity in the first-order formalism, also including fermions. However, the resulting fermion-gravity coupling deviates from the conventional form, explicitly violating parity and time-reversal symmetries. Additionally, these fermions exhibit an unconventional transformation behavior under $SO(2)$ transformations. Furthermore, we analyze the consistency of this mapping at the quantum level using the path integral formalism and Becchi-Rouet-Stora-Tyutin techniques. Our findings demonstrate that quantum electrodynamics and quantum gravity remain equivalent at the quantum level.