黑洞时空中规范场的Hamilton BRST形式
Hamiltonian BRST formalism for gauge fields on black hole spacetimes
摘要：
本文研究了球对称黑洞时空中的Becchi-Rouet-Stora-Tybern（BRST）规范理论，包括有无宇宙学常数（$Λ\geq0$）.这是通过标量电动力学的例子说明。我们首先证明，视界贡献额外的表面条款的高斯定律约束的理论时，规范变换不需要消失的视野。然后，我们考虑BRST不变的路径积分，包括这些表面项以下的哈密顿BRST形式主义。我们固定了一个类辐射规范，其中涉及零分量的电磁场在地平线上。我们发现，存在的表面条款的约束力的鬼和规范固定行动，包括额外的表面积分的视野。在视界处的规范场的零组合被示出为通过视界处的附加项来修改理论的鬼数荷。我们还演示了如何可以构建一个规范固定费米子产生自己的幂零对称变换，称为共BRST变换，离开理论不变。BRST和合作BRST变换进一步用于确定穿着（规范不变）领域的理论，其敷料的存在下的杀戮地平线的影响。最后，我们讨论了我们的结果在软极限和热场论的黑洞背景的潜在应用。
英文摘要：
We investigate the Becchi-Rouet-Stora-Tyutin (BRST) formalism for gauge theories on spherically symmetric black hole spacetimes, with or without a cosmological constant ($Λ\geq0$). This is illustrated through the example of scalar electrodynamics. We first demonstrate that the horizons contribute additional surface terms to the Gauss law constraint of the theory when gauge transformations are not required to vanish on the horizons. We then consider the BRST invariant path integral including these surface terms following the Hamiltonian BRST formalism. We fix a radiation-like gauge which involves null components of the electromagnetic field at the horizons. We find that the presence of the surface terms in the constraint forces the ghost and gauge fixing actions to include additional surface integrals at the horizons. The null combination of the gauge fields at the horizons is shown to modify the ghost number charge of the theory through additional terms at the horizons. We also demonstrate how one can construct a gauge-fixing fermion which generates its own nilpotent symmetry transformations, called co-BRST transformations, that leave the theory invariant. The BRST and co-BRST transformations are further used to identify dressed (gauge invariant) fields of theory, whose dressings are affected by the presence of Killing horizons. We conclude with a discussion of potential applications of our results in soft limits and thermal field theories on black hole backgrounds.
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