带域上Maxwell-Chern-Simons理论中的边缘物理与卡西米尔相互作用
Edge physics and the Casimir interaction in Maxwell-Chern-Simons theory on a strip
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中文总结 AI 辅助
研究带域上Maxwell-Chern-Simons理论的边缘物理，推导其边界条件与流代数，得到有限相互作用能的行列式表示，分析Maxwell极限与含拓扑质量时的卡西米尔力特性。
中文摘要 AI 辅助
我们在含边界量子场论的Symanzik框架下，研究带域$\boldsymbol{\relax M=\reals^{1,1}\times[0,h]}$上的Maxwell-Chern-Simons理论。我们添加全论文采用的二次单切向导数截断内最一般的定域边界泛函，通过定域性与变分原理推导容许的边界条件，其中规范对称性通过边界沃德恒等式实现。该带域支持两个边界$\boldsymbol{U(1)}$流代数，其相反级数由Chern-Simons耦合$\boldsymbol{\relax\beta}$和边界取向确定，而边缘速度依赖于局域边界耦合；在翻转对称分支上它们大小相等、方向相反，这是空间对称带域的自然选择。相同边界数据确定体模的反射系数，给出有限相互作用能的闭合行列式（散射）表示。在Maxwell极限（$\boldsymbol{\relax\beta=0}$）下，边缘间相互作用为长程，产生幂律卡西米尔力；而在Maxwell-Chern-Simons理论中，拓扑质量$\boldsymbol{\relax m=\beta g^2}$在大间距$\boldsymbol{\relax mh\biggg1}$时产生汤川抑制。行列式形式还可解析控制渐近区域，将拓扑边界数据（级数与反常流入）与动力学体效应（色散、边界混合及卡西米尔相互作用）分离。
英文摘要
We study how boundaries affect Maxwell-Chern-Simons theory, a three-dimensional gauge theory that combines ordinary electromagnetic propagation with a topological Chern-Simons term. On a strip, the two boundaries can support edge excitations while the single massive bulk mode mediates a Casimir interaction between them. We use Symanzik's local boundary-field-theory framework, deriving the boundary conditions from the most general quadratic local boundary action considered here rather than imposing them by hand. Requiring these conditions to act consistently on the unique physical bulk mode selects a continuous family of admissible boundaries, characterized by an impedance and an edge velocity. The associated conserved currents form two boundary current algebras with opposite levels, and for a symmetric strip the edge modes propagate in opposite directions. The bulk and residual edge sectors factorize, leaving a single physical scattering channel for the Casimir problem. We derive its reflection amplitude, identify a stable pole-free domain, and show that the force is attractive there. In the Maxwell limit the usual long-range one-channel Casimir interaction is recovered, whereas the topological mass produces exponential screening at large separation. Outside the pole-free domain, localized surface modes can appear and must be included separately. The analysis provides a unified description of edge dynamics, boundary conditions and vacuum forces in a topologically massive gauge theory.
