Entanglement in Quantum Field Theory

• Main Authors: Chen-Te Ma, 馬承德
• Other Authors: Kazuo Hosomichi
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/y8ft75

博士 === 國立臺灣大學 === 物理學研究所 === 107 === 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.