论文标题
麦克斯韦球场带有量规固定术语在de Sitter空间中：精确的解决方案和应力张量
Maxwell field with gauge fixing term in de Sitter space: exact solution and stress tensor
论文作者
论文摘要
具有通用量规固定（GF）项的麦克斯韦场是不平凡的，不仅在场方程中混合了纵向和时间模式，而且GF项也可能产生不必要的后果。我们在DE Sitter空间中得出了完整的解决方案集，并实施了协变量的规范量化，该量子将残余规变速器限制为量子剩余量规变换。然后，在Gupta-Bleuler（GB）物理状态中，我们计算了应力张量，该应力张量非常独立于量规固定常数，并且在量子残差量规变换下也是不变的。 横向组件与Minkowski时空中的成分仅相同，并且横向真空应力张量只有一个紫外线发散项（$ \ propto k^4 $），该项被0阶绝热正则化而变为零。由于纵向和颞部之间的取消，GB状态的纵向 - 周期性应力张量为零。更有趣的是GF项的应力张量。由于GB状态取消，其粒子贡献为零，其真空贡献是最小耦合无质量标量场的两倍，其中包含$ k^4 $和$ k^2 $ divergences。二阶绝热正则化后，GF真空应力张量也变为零，因此无需引入幽灵场，而零GF真空应力张量不能成为宇宙学常数的候选者。因此，麦克斯韦（Maxwell Field）带有GF项所预测的所有物理学将与没有GF项的物理学相同。我们还在Minkowski时空进行了类似的计算，并且应力张量与DE Sitter空间相似，但比DE Sitter更简单。
The Maxwell field with a general gauge fixing (GF) term is nontrivial, not only the longitudinal and temporal modes are mixed up in the field equations, but also unwanted consequences might arise from the GF term. We derive the complete set of solutions in de Sitter space, and implement the covariant canonical quantization which restricts the residual gauge transformation down to a quantum residual gauge transformation. Then, in the Gupta-Bleuler (GB) physical state, we calculate the stress tensor which is amazingly independent of the gauge fixing constant and is also invariant under the quantum residual gauge transformation. The transverse components are simply the same as those in the Minkowski spacetime, and the transverse vacuum stress tensor has only one UV divergent term ($\propto k^4$), which becomes zero by the 0th-order adiabatic regularization. The longitudinal-temporal stress tensor in the GB state is zero due to a cancelation between the longitudinal and temporal parts. More interesting is the stress tensor of the GF term. Its particle contribution is zero due to the cancelation in the GB state, and its vacuum contribution is twice that of a minimally-coupling massless scalar field, containing $k^4$ and $k^2$ divergences. After the 2nd-order adiabatic regularization, the GF vacuum stress tensor becomes zero too, so that there is no need to introduce a ghost field, and the zero GF vacuum stress tensor can not be a possible candidate for the cosmological constant. Thus, all the physics predicted by the Maxwell field with the GF term will be the same as that without the GF term. We also carry out analogous calculation in the Minkowski spacetime, and the stress tensor is similar to, but simpler than that in de Sitter space.
