论文标题
从Euler-Arnold方程中的保形场理论复杂性
Conformal field theory complexity from Euler-Arnold equations
论文作者
论文摘要
定义量子场理论中的复杂性是一项艰巨的任务，主要挑战涉及自由模型以及相关的高斯州和操作。一个问题的一种是考虑1+1维度中的保形场理论，我们的工作是对其能量弹药量的通用部门的国家和运营商复杂性的全面研究。统一的概念思想是Euler-Arnold方程及其差异性概括，它们可以保证两个通用状态或感兴趣的转变之间的优化问题的良好性。目前的工作对Arxiv：2005.02415中报道的结果及其推导中使用的技术进行了深入的讨论。我们涵盖的最重要的主题之一是使用差分正则化，这是描述fubini-study态复杂性并探测潜在几何形状的整数分化方程的解决方案。
Defining complexity in quantum field theory is a difficult task, and the main challenge concerns going beyond free models and associated Gaussian states and operations. One take on this issue is to consider conformal field theories in 1+1 dimensions and our work is a comprehensive study of state and operator complexity in the universal sector of their energy-momentum tensor. The unifying conceptual ideas are Euler-Arnold equations and their integro-differential generalization, which guarantee well-posedness of the optimization problem between two generic states or transformations of interest. The present work provides an in-depth discussion of the results reported in arXiv:2005.02415 and techniques used in their derivation. Among the most important topics we cover are usage of differential regularization, solution of the integro-differential equation describing Fubini-Study state complexity and probing the underlying geometry.
