This work investigates the classical and quantum duality between the -Maxwell-Chern-Simons (MCS) model and its self-dual counterpart. Initially, we focus on free-field cases to establish equivalence through two distinct approaches: comparing the equations of motion and utilizing the master Lagrangian method. In both instances, the classical correspondence between the self-dual and MCS dual fields undergoes modifications due to very special relativity (VSR). Specifically, the duality is established when the associated VSR-mass parameters are identical, and the dual field is introduced through a non-local VSR correction. Furthermore, we analyze the duality when the self-dual model is minimally coupled to fermions. As a result, we demonstrate that Thirring-like interactions, corrected for non-local VSR contributions, are included in the MCS model. Additionally, we establish the quantum equivalence of the models by performing a functional integration of the fields and comparing the resulting effective Lagrangians.

中文翻译：

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狭义相对论中麦克斯韦-陈-西蒙斯和自对偶模型之间的对偶性


这项工作研究了 -Maxwell-Chern-Simons (MCS) 模型与其自对偶模型之间的经典和量子对偶性。最初，我们专注于自由场情况，通过两种不同的方法建立等效性：比较运动方程和利用主拉格朗日方法。在这两种情况下，自对偶场和 MCS 对偶场之间的经典对应关系都会因狭义相对论 (VSR) 而发生修改。具体地，当相关的VSR质量参数相同时，对偶性建立，并且通过非局部VSR校正引入对偶场。此外，我们分析了自对偶模型与费米子最小耦合时的对偶性。结果，我们证明了 MCS 模型中包含了类似 Thirring 的相互作用，并针对非局部 VSR 贡献进行了校正。此外，我们通过对场进行函数积分并比较所得的有效拉格朗日量来建立模型的量子等价性。