arXiv 2010.154452020-10gr-qchep-th

广义统计平衡与离散量子引力

On Generalised Statistical Equilibrium and Discrete Quantum Gravity

Isha Kotecha

备注：: PhD thesis, Humboldt University of Berlin, Albert Einstein Institute - Potsdam; v2 few minor changes and updated references, to be published in Springer Theses book series

摘要：

统计平衡位形在具有大量组成自由度的宏观系统的物理学中是重要的。它们在离散的量子引力中也是至关重要的，在离散的量子引力中，动力学时空应该从量子引力自由度的集体物理中产生。然而，在背景独立系统中定义统计平衡是一个具有挑战性的开放问题，主要是由于缺乏绝对的时间和能量概念。这在没有通常的空间和时间结构的非微扰量子引力框架中尤其如此。在这篇论文中，我们调查的统计平衡，特别是吉布斯状态，适用于背景独立系统的概括方面。我们强调基于最大熵原理的信息论表征。随后，我们探讨了由此产生的广义吉布斯态在一个离散的量子引力系统组成的许多候选量子的几何形状，利用他们的场论制定的群场论和各种多体技术。我们构造了几个量子引力广义吉布斯态的具体例子。我们进一步发展不等价的热表示的基础上纠缠，双模压缩，热场双真空，诱导一类广义吉布斯状态。在这些表示中，我们定义了一类热凝聚体，它在给定的可观测量中编码统计波动，例如量子几何的体积。我们将这些状态应用于群场论的凝聚宇宙学方案中，研究了从一类自由模型中提取的均匀各向同性时空的相关有效宇宙动力学。我们发现正确的经典极限的弗里德曼方程在后期，反弹和加速膨胀的早期。

英文摘要：

Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete quantum gravity, where dynamical spacetime should emerge from the collective physics of the underlying quantum gravitational degrees of freedom. However, defining statistical equilibrium in a background independent system is a challenging open issue, mainly due to the absence of absolute notions of time and energy. This is especially so in non-perturbative quantum gravity frameworks that are devoid of usual space and time structures. In this thesis, we investigate aspects of a generalisation of statistical equilibrium, specifically Gibbs states, suitable for background independent systems. We emphasise on an information theoretic characterisation based on the maximum entropy principle. Subsequently, we explore the resultant generalised Gibbs states in a discrete quantum gravitational system composed of many candidate quanta of geometry, utilising their field theoretic formulation of group field theory and various many-body techniques. We construct several concrete examples of quantum gravitational generalised Gibbs states. We further develop inequivalent thermal representations based on entangled, two-mode squeezed, thermofield double vacua, induced by a class of generalised Gibbs states. In these representations, we define a class of thermal condensates which encode statistical fluctuations in a given observable, e.g. volume of the quantum geometry. We apply these states in the condensate cosmology programme of group field theory to study a relational effective cosmological dynamics extracted from a class of free models, for homogeneous and isotropic spacetimes. We find the correct classical limit of Friedmann equations at late times, with a bounce and accelerated expansion at early times.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文