标题： 高阶陈-西蒙斯在$2+1$维空间中的量子电动力学扩展 显示英文标题

标题： Higher-order Chern-Simons extensions to QED in $2+1$ dimensions

摘要： 在本工作中，我们研究了在$2+1$维度下与标准旋量物质耦合的麦克斯韦-陈-西蒙斯模型的高阶扩展中的辐射修正。 我们首先分析高阶规范场部分，在其中我们找到了与质量光子和鬼场相关的模式和极化矢量。 高阶规范模型被经典地量子化，正如预期的那样，产生的产生和湮灭算符的代数对应于希尔伯特空间中的不定度规。 随后，我们从费米子自能开始，计算修改后的QED中所有相关的单环图。 我们表明，对费米子两点函数的诱导修正产生了两个独立的费米子自由度，这些可以包含在一个重新定义的拉格朗日量中，该拉格朗日量描述了两个解耦的费米子场，一个对应于物理粒子，另一个对应于负范数的鬼态。 我们利用这种分解来计算光子极化算符和顶点修正，两者都被发现是有限的。 最后，我们通过计算不同时空点处规范场的对易子来分析模型的因果行为，并发现微观因果性得到了保持。 显示英文摘要

摘要： In this work, we investigate radiative corrections in the higher-order extension of the Maxwell-Chern-Simons model coupled to standard spinor matter in $2+1$ dimensions. We begin analyzing the higher-order gauge sector, where we find the modes and the polarizations vectors associated to a massive photon and ghost field. The higher-order gauge model is canonically quantized and as expected the resulting algebra of creation and annihilation operators corresponds to an indefinite metric in Hilbert space. Subsequently, we compute all relevant one-loop diagrams in the modified QED starting with the fermion self-energy. We show that the induced corrections to the fermion two-point function produce two independent fermionic degrees of freedom, which can be included in a redefined Lagrangian describing two decoupled fermions fields, one corresponding to a physical particle and the other to a negative-norm ghost state. We take advantage of this decomposition to compute the photon polarization operator and the vertex correction, both of which are found to be finite. Finally, we analyze the causal behavior of the model by computing the commutator of gauge fields at different spacetime points, and found that microcausality is preserved.