双锥中无质量Majorana场的Bell-CHSH违背：基于模局域化的研究
Bell-CHSH Violation for a Massless Majorana Field in a Double Cone from Modular Localization
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中文总结 AI 辅助
本文研究双锥中无质量Majorana场的Bell-CHSH关联，利用模局域化导出相关算子与正交关系，发现高斯模动量剖面下Bell参数可超经典边界并趋近Tsirelson值，得到近最大Bell违背。
中文摘要 AI 辅助
我们研究局域在双锥中的手征无质量Majorana场的Bell-CHSH关联。将相关光射线区间的共形模流转换为快度类坐标的平移，并在模动量空间中导出单粒子标量积，特别关注该标量积带有费米-狄拉克权重这一事实。要求模共轭关于该加权标量积是反幺正的，这确定了模对象的傅里叶空间实现。所得的Tomita-Takesaki算子及其伴随算子生成Alice和扭曲对偶Bob方向，所有四个交叉CAR正交关系自动由模局域化导出。Bell问题随后简化为单函数泛函。对于高斯模动量剖面$h_\sigma(k)=\exp[-k^2/(2\sigma^2)]$，在宽范围的宽度内，Bell参数大于经典边界，并解析地趋近于Tsirelson值$\lim_{\sigma\to 0^+}{\it B}(\sigma)=2\sqrt2$。因此，从集中在零模动量附近的光滑速降剖面的显式序列中获得近最大Bell违背，对应于模谱值$\lambda=1$。
英文摘要
We investigate Bell-CHSH correlations for a chiral massless Majorana field localized in a double cone. The conformal modular flow of the associated light-ray interval is converted into translations by a rapidity-like coordinate, and the one-particle scalar product is derived in modular momentum space. Particular attention is paid to the fact that this scalar product carries a Fermi-Dirac weight. Requiring the modular conjugation to be antiunitary with respect to that weighted scalar product fixes the Fourier-space realization of the modular objects. The resulting Tomita-Takesaki operator and its adjoint generate Alice and twisted-dual Bob directions for which all four crossed CAR orthogonality relations follow automatically from modular localization. The Bell problem then reduces to a simple one-function functional. For a Gaussian modular-momentum profile $h_σ(k)=\exp[-k^2/(2σ^2)]$ the Bell parameter is larger than the classical bound for a broad range of widths and approaches the Tsirelson value analytically, \[ \lim_{σ\to 0^+}{\it B}(σ)=2\sqrt2 \] Thus near-maximal Bell violation is obtained from an explicit sequence of smooth rapidly decreasing profiles concentrated around zero modular momentum, corresponding to the modular spectral value $λ=1$.
