Astro-Particule et Cosmologie, Université Paris 7-Denis Diderot, 10 rue Alice Domont et Léonie Duquet, 75205 Paris cedex 13, France.
Phys Rev Lett. 2011 Nov 4;107(19):191103. doi: 10.1103/PhysRevLett.107.191103. Epub 2011 Nov 3.
We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken symmetry state in any dimension.
我们在非微扰的 1/N 展开中研究了在 de Sitter 几何中的 O(N)标量场的量子理论。这对所谓的超雏菊环图的无限级数进行了重整化。我们得到了相应的、适当正则化的动力学场方程的 de Sitter 对称解，并计算了完整的有效势。由于其自相互作用，场获得了严格为正的平方质量，从而屏蔽了潜在的红外发散。此外，强烈增强的超长波长涨落阻止了在任何维度下存在自发破缺对称的状态。
