摘要
規範理論中的糾纏在希爾伯特空間的張量積分解中很難定義，所以我們有興趣從中心去理解希爾伯特空間的非張量積分解中的糾纏，該中心與希爾伯特空間中的所有運算符可交換。我們一開始討論部分跡的運算和不等式以及中心的數學特性，特別是強亞可加性。然後我們考慮哈密頓方法，證明在 2p + 2 維 p-型非相互作用理論中糾纏熵的電和磁的選擇是相同的，並且提出用拉格朗日公式計算中心的糾纏熵。我們使用複制技巧來計算愛因斯坦希爾伯特引力理論中的糾纏熵，並在 2p + 2 維中 p-形式的非相互作用理論中的糾纏熵的通用項重寫成偶數維度 0 形式的非交互作用理論的熵的通用項。特別地，我們討論了二維愛因斯坦 - 希爾伯特引力理論中糾纏熵中的余維數二的面，並討論了糾纏熵的非體積定律與平移不變性之間的關係。最後，我們證明了二維保形場理論在一些特殊情況下的糾纏熵的通用項和互信息不依賴於中心的選擇。
並列摘要
Entanglement in gauge theories is hard define in a tensor product decomposition of a Hilbert space so we are interested in understanding the entanglement in a non-tensor product decomposition of a Hilbert space from centers, which commute with all operators in the Hilbert space. We begin with discussing mathematical properties of a partial trace operation and inequalities with the centers, especially the strong subadditivity. Then we consider the Hamiltonian method to show that the electric and magnetic choices of the entanglement entropy in non-interacting theories of the p-form in 2p+2 dimensions are the same and also propose the Lagrangian formulation to compute the entanglement entropy with centers. We use the replica trick to compute the entanglement entropy in the Einstein-Hilbert gravity theory and rewrite universal terms of the entanglement entropy in non-interacting theory of the p-form in 2p+2 dimensions in terms of universal terms of the entanglement entropy in the non-interacting theory of the 0-form in even dimensions. Especially, we discuss a codimension two surface term in the entanglement entropy in the two dimensional Einstein-Hilbert gravity theory and also discuss a relation between a non-volume law of the entanglement entropy and the translational invariance. Finally, we prove that universal terms of the entanglement entropy and mutual information in some special cases of two dimensional conformal field theory do not depend on a choice of centers.