在本文中，我們將回顧量子場論中的糾纏熵。我們想通過一些物理例子
給出糾纏熵的詳細計算。此外，我們還尋找了糾纏熵的推廣模型，如偽熵，
並提供了逐步計算方法以得到結果並嘗試了解其背後的意義

In this thesis, we will give an overview of entanglement entropy (EE) in quantum field theory. We aim to present detailed calculations of EE in several physical examples. In addition, we will review generalized models of entanglement entropy, such as pseudo entropy, and provide a step-by-step calculation method to obtain the entropy.

1 Introduction 1
2 Entanglement entropy 2
2.1 Introduction to the entanglement entropy . . . . . . . . . . . . . . . . . . . . . 2
2.2 Two coupled harmonic oscillators . . . . . . . . . . . . . . . . . . . . . . . . 3
2.3 Free scalar field theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Entropy and area law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Entanglement entropy in two dimensional CFT and replica trick . . . . . . . . 14
3 Pseudo Entropy 22
3.1 Introduction to the pseudo entropy . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 Cosmological expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Correlator method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.4 Operator method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5 Pseudo entropy in two dimensional CFT . . . . . . . . . . . . . . . . . . . . . 43
4 Conclusion 45
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
I Symplectic geometry and Williamson’s Theorem . . . . . . . . . . . . . . . . 48
References 51

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