2012/11/30 by Daisuke Ida, Takahiro Okamoto, Miyuki Saito
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Casimir element #Conformal field theory #Minkowski space #Noncommutative and Quantum Gravity Theories #Open quantum system #Quantum Electrodynamics and Casimir Effect #Quantum discord #Quantum entanglement #Quantum field theory #Scalar field #Vacuum state #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.1093/ptep/ptt061
11 pages, 2 figures
arxiv created 2013/06/21 · openalex publication_date 2013/08/01 · arxiv updated 2016/06/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the quantum state seen by an observer in a diamond-shaped region, which is a globally hyperbolic open submanifold of Minkowski space-time. It is known from the operator-algebraic argument that the vacuum state of the quantum field transforming covariantly under the conformal group looks like a thermal state on the von Neumann algebra generated by the field operators on the diamond-shaped region of Minkowski space-time. Here, we find, in the case of the free massless Hermitian scalar field in 2D Minkowski space-time, that such a state can in fact be identified with a certain entangled quantum state. By doing this, we obtain thermodynamic quantities such as the Casimir energy and the von Neumann entropy of the thermal state in the diamond-shaped region, and show that the Bekenstein bound for the entropy-to-energy ratio is saturated. We further speculate on a possible information-theoretic interpretation of the entropy in terms of the probability density functions naturally determined from the Tomita–Takesaki modular flow in the diamond-shaped region.