标题： Hilbert空间形式化用于群场理论 显示英文标题

标题： Hilbert space formalisms for group field theory

摘要： 群场理论是量子引力的一种背景独立方法，其出发点是在辅助群流形上定义一个量子场论（不被解释为时空，而是被解释为单个“几何原子”的有限维配置空间）。 群场理论模型可以看作是通过附加数据对矩阵和张量模型的扩展，并且传统上通过一个泛函积分来定义，其微扰展开生成离散几何的求和。 最近，一些努力集中在基于希尔伯特空间和算子的群场理论公式上，特别是在宇宙学应用中。 这是对这些公式及其主要思想的尝试性综述，尽可能将这些构造与应用和现象学分离，并将它们置于更广泛的量子引力研究背景中。 显示英文摘要

摘要： Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional configuration space of a single "atom" of geometry). Group field theory models can be seen as an extension of matrix and tensor models by additional data, and are traditionally defined through a functional integral whose perturbative expansion generates a sum over discrete geometries. More recently, some efforts have been directed towards formulations of group field theory based on a Hilbert space and operators, in particular in applications to cosmology. This is an attempt to review some of these formulations and their main ideas, to disentangle these constructions as much as possible from applications and phenomenology, and to put them into a wider context of quantum gravity research.