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Time ordering, Wick rotation and analyticity

Physicists learn from junior field theory courses (if not kindergarten) that

  • In Minkowski spacetime, expectation of field operators calculated by path integral is time ordered.
  • One can perform a ‘Wick rotation’ to transform ‘real time’ in Minkowski space to ‘imaginary time’ in Euclidean space.

In this post, we are going to clarify the effectiveness and limitation of the statements above by consideration of analyticity. The main idea in this post comes from Witten’s note1, Xi Yin’s lecture in Harvard2 and informal discussions with my advisor Yingfei Gu.

  1. Witten, E., 2018. Notes on Some Entanglement Properties of Quantum Field Theory. Rev. Mod. Phys. 90, 045003. https://doi.org/10.1103/RevModPhys.90.045003

  2. You can find lecture notes on https://sites.google.com/view/xi-yin/qft-notes?authuser=0&pli=1

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北京

夕阳涂抹城市,颜料干涩
北四环从棱角分明的格子里长出
涌向太阳的钢铁咆哮
淹没自行车的抒情
——自行车抒情时
生锈的链子会吱吱呀呀地叫

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LaTeX 入门

LaTeX 是一款排版软件, 常用于理工科专业文档的排版. 这篇文档旨在提供一个不完整但容易上手的、现代的入门指引. 我认为学习一项技术, 尤其是一种工具, 最有效的方式并不是去阅读一本完整的教程, 而是直接去动手实践, 在实践中逐步学习需要的部分. 作为一款排版软件, LaTeX 的试错成本尤其低廉 (可能只是编译失败一次需要的时间和电量吧), 所以更适合如此入门.

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Connections in physics

Modern differential geometry provides a unified picture for different aspects of physics. In this blog article I would like to introduce three kinds of physical subjects relating to connection on a fibre bundle, namely gauge field, general relativity and theory of quantum Hall effect. The ‘gauge field’ part is among the appendices of my undergraduate thesis.

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清明

我是否可以这样开头
而不算亵渎:四月最残忍1
没有下雨的清明,午后平凡而臃肿
楼前桃花鲜艳,阳光给漆成淡粉色的
宿舍外墙打上过时的粉底
自行车棚绿色的顶无意遮蔽
精细组织起来的橡胶和金属
铃声可能曾被看作一个惊喜的来源
眼睛里的光泛起或失落,太阳继续下移
女生宿舍楼下晾晒的床单被罩
是播放私人电影的幕布——他在电视剧里
看到过这样的情节:警察出现
小流氓逃窜,他从未拉过女孩的手
风吹起床单和远处她的头发
这会是哪个时代的故事?

  1. 见艾略特《荒原》首句。 

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北京大学图书馆

北京大学图书馆
东厅,灯光明亮
方木桌子大而重
表面光滑,放着
同样光滑的笔记本电脑
高分辨率的屏幕上
无衬线字体抛光底格里斯的河床

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