发表机构
Faculdade de Física, Universidade Federal do Pará（帕拉联邦大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过维度约化得到伪CFJ理论，求解其静态势并证明其违反幺正性，与PQED形成对比。
AI 中文摘要
我们研究了Carroll-Field-Jackiw（CFJ）理论从(3+1)维到(2+1)维的维度约化。所得有效场论称为伪CFJ（PCFJ）理论，展现出由嵌套伪微分算子控制的复杂非局域结构。我们精确求解了静态相互作用势，揭示了库仑型短距离行为和由拓扑有效质量决定的修正汤川长距离衰减。最后，通过应用广义光学定理，我们严格证明了PCFJ理论违反幺正性，这与原生伪量子电动力学（PQED）形成鲜明对比。
英文摘要
This article investigates the dimensional reduction of the massive Carroll-Field-Jackiw (CFJ) theory from $(3+1)D$ to $(2+1)D$ dimensions with the objective of constructing and analyzing the resulting effective field theory, termed pseudo-Carroll-Field-Jackiw (PCFJ). The theoretical framework relies on quantum field theory, pseudo-quantum electrodynamics (PQED) and Lorentz-violating models. The methodological procedure projects the three-dimensional dynamics onto the plane by rigorously integrating out the gauge field degrees of freedom along the transverse momentum. Subsequently, the study calculates the static interaction potential, applies both the generalized optical theorem and the Källén-Lehmann spectral representation to test probability conservation. The results reveal that the effective theory exhibits an intricate non-local structure, governed by nested pseudo-differential operators, which generates a static potential that transitions from a Coulomb-like behavior at short distances to a long-range decay modified by a topological mass. The research analytically proves that the integration of the extra-dimensional topology introduces ineliminable branch cuts in momentum space, which preclude the causal definition of asymptotic states and determine the breakdown of unitarity. The work concludes that this quantum instability emerges from the direct interplay between the spatial projection and the pre-existing Lorentz-violating background in the bulk.
