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Exploring the entanglement of free spin-(1/2), spin-1 and spin-2 fields

Exploring the entanglement of free spin-(1/2), spin-1 and spin-2 fields
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摘要 In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method. In this study, we explore the entanglement of free spin-(1/2), spin-1, and spin-2 fields. We start with an example involving Majorana fields in 1+1 and 2+1 dimensions. Subsequently, we perform the Bogoliubov transformation and express the vacuum state with a particle pair state in the configuration space, which is used to calculate the entropy. This clearly demonstrates that the entanglement entropy originates from the particles across the boundary.Finally, we generalize this method to free spin-1 and spin-2 fields. These higher free massless spin fields have wellknown complications owing to gauge redundancy. We deal with the redundancy by gauge-fixing in the light-cone gauge. We show that this gauge provides a natural tensor product structure in the Hilbert space, while surrendering explicit Lorentz invariance. We also use the Bogoliubov transformation to calculate the entropy. The area law emerges naturally by this method.
作者 Zhi Yang Ling-Yan Hung 杨智;孔令欣(Department of Physics & Center for Field Theory and Particle Physics, Fudan University;State Key Laboratory of Surface Physics & Department of Physics, Fudan University)
出处 《Chinese Physics C》 SCIE CAS CSCD 2019年第5期12-22,共11页 中国物理C(英文版)
基金 Supported by the NSFC(11875111)
关键词 ENTANGLEMENT BOGOLIUBOV transformation TENSOR product structure entanglement Bogoliubov transformation tensor product structure
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