论文标题
费米子量子场理论的相对熵
Relative Entropy for Fermionic Quantum Field Theory
论文作者
论文摘要
我们从Araki的意义上研究了相对熵，以表示自偶尔汽车代数$ \ mathfrak {a} _ {sdc}（\ Mathcal {h}，γ）$。我们注意到，对于\ Mathcal {H} $的$ f \的特定选择，$ \ Mathfrak中的关联元素{a} _ {sdc}（\ Mathcal {h}，γ）$是统一的。结果，我们明确计算了$ \ mathfrak {a} _ {sdc}（\ mathcal {h}，γ）$与$ \ mathfrak {a} _ {a}，γ）$之间的相对熵与相对于上述单位元素的激发。该方法的一般性使我们可以将$ \ Mathcal {H} $视为在全球双曲线上的经典狄拉克方程解决方案的希尔伯特解决方案，这使我们的结果是对费米昂量子场理论的相对熵的计算。我们的结果扩展了Longo和Casini等人的结果。对于自由标量量子场理论的准确态与相干激发之间的相对熵，对于费米子。作为第一个应用程序，我们计算了超级时空上Majorana场的相对熵。
We study the relative entropy, in the sense of Araki, for the representation of a self-dual CAR algebra $\mathfrak{A}_{SDC}(\mathcal{H},Γ)$. We notice, for a specific choice of $f \in \mathcal{H}$, that the associated element in $\mathfrak{A}_{SDC}(\mathcal{H},Γ)$ is unitary. As a consequence, we explicitly compute the relative entropy between a quasifree state over $\mathfrak{A}_{SDC}(\mathcal{H},Γ)$ and an excitation of it with respect to the abovely mentioned unitary element. The generality of the approach, allows us to consider $\mathcal{H}$ as the Hilbert space of solutions of the classical Dirac equation over globally hyperbolic spacetimes, making our result, a computation of relative entropy for a Fermionic Quantum Field Theory. Our result extends those of Longo and Casini et al. for the relative entropy between a quasifree state and a coherent excitation for a free Scalar Quantum Field Theory, to the case of fermions. As a first application, we computed such a relative entropy for a Majorana field on an ultrastatic spacetime.
