标题： Hartree近似在弯曲时空中的再探讨 I: de Sitter中的有效势 显示英文标题

标题： The Hartree approximation in curved spacetimes revisited I: the effective potential in de Sitter

摘要： 我们考虑了一个在弯曲时空中的具有{\lambda }{\phi } ^4 相互作用的量子标量场。 通过Hartree近似于2PI有效作用量的方法，非微扰地考虑了量子效应。 尽管这种近似在许多先前的研究中已被考虑过，但我们使用了一致的非微扰重整化过程重新考虑它，并将其推广到一般的弯曲时空中。 我们得到了平均场和涨动传播子的重整化方程，明确展示了它们与由正则化方案引入的任意尺度的独立性。 我们将结果应用于特定的 de Sitter 时空情况，并讨论自发对称破缺。 结果强烈依赖于重整化过程。 显示英文摘要

摘要： We consider a quantum scalar field with {\lambda}{\phi}^4 interaction in curved spacetimes. The quantum effects are taken into account nonperturbatively using the Hartree approximation to the 2PI effective action. Although this approximation has been considered in many previous works, we reconsider it using a consistent nonperturbative renormalization procedure, which we extend to general curved spacetimes. We obtain the renormalized equations for the mean field and for the propagator of the fluctuations, showing explicitly their independence on the arbitrary scale introduced by the regularization scheme. We apply our results to the particular case of de Sitter spacetime and discuss spontaneous symmetry breaking. The results depend strongly on the renormalization procedure.