Exploring the entanglement of free spin-${\bf\dfrac{1}{2}}$, spin-1 and spin-2 fields

• In this study, we explore the entanglement of free spin-$\displaystyle\frac{1}{2}$, 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 well-known 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.
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Zhi Yang and Ling-Yan Hung. Exploring the entanglement of free spin-${\bf\dfrac{1}{2}}$, spin-1 and spin-2 fields[J]. Chinese Physics C, 2019, 43(5): 053102-1-053102-11. doi: 10.1088/1674-1137/43/5/053102
Zhi Yang and Ling-Yan Hung. Exploring the entanglement of free spin-${\bf\dfrac{1}{2}}$, spin-1 and spin-2 fields[J]. Chinese Physics C, 2019, 43(5): 053102-1-053102-11.
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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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Exploring the entanglement of free spin-${\bf\dfrac{1}{2}}$, spin-1 and spin-2 fields

• 1. Department of Physics & Center for Field Theory and Particle Physics, Fudan University, 200433 Shanghai, China
• 2. State Key Laboratory of Surface Physics & Department of Physics, Fudan University, 200433 Shanghai, China

Abstract: In this study, we explore the entanglement of free spin-$\displaystyle\frac{1}{2}$, 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 well-known 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.

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