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.
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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. ↩
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You can find lecture notes on https://sites.google.com/view/xi-yin/qft-notes?authuser=0&pli=1. ↩
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.
36 post articles, 5 pages.