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arXiv 0710.4880hep-phcond-mat.other
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QED_{3}的扰动和非扰动方面

Perturbative and non-perturbative aspects of QED_{3}

Sergej Moroz

摘要:

本文综述了平面量子物理中的各种发现,特别是三维时空中的双分量量子电动力学(QED_{3})和Chern-Simons(CS)项。首先简要介绍了经典电动力学。然后我们构造并分类了庞加莱群的酉不可约表示,并将它们与各种协变域联系起来。还讨论了QED_{3}中离散对称性的微妙之处。在库仑规范中对有无CS项的自由规范场进行了量子化。随后,我们讨论了微扰区理论的紫外行为,并进行了单圈计算。诱导CS长期使用有效的行动形式主义。在Maxwell-Chern-Simons理论中考虑了非相对论性的电子-电子相互作用,并简要讨论了束缚态的可能性。我们还研究了非相对论散射的两个任意子在纯CS理论的单圈秩序。

英文摘要:

In this work we review various findings in the planar quantum physics with the special emphasis on the two-component quantum electrodynamics in three-dimensional spacetime (QED_{3}) with the Chern-Simons (CS) term. First the classical electrodynamics is briefly outlined. Then we construct and classify the unitary irreducible representations of the Poincare group and connect them to various covariant fields. Subtleties with discrete symmetries arising in QED_{3} are also discussed. Quantization of the free gauge field with and without the CS term is performed in Coulomb gauge. Subsequently we discuss the ultraviolet behavior of the theory in perturbative regime and perform some one-loop calculations. The induced CS term is examined using the effective action formalism. The non-relativistic electron-electron interactions are considered in the Maxwell-Chern-Simons theory and the possibility of bound states is briefly discussed. We also examine the non-relativistic scattering of two anyons in the pure CS theory to one-loop order.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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