Møller算子与带MIT边界条件的Dirac场的Hadamard态
Møller operators and Hadamard states for Dirac fields with MIT boundary conditions
AI总结：
本文通过引入几何Møller算子，证明了在具类时边界的全局双曲流形上带MIT边界条件的Dirac场的Hadamard态的存在性，并展示了其两点分布奇性结构的保持。
摘要：
本文旨在证明在任何具有类时边界的全局双曲流形上，与MIT边界条件耦合的Dirac场的Hadamard态的存在性。这是通过引入几何Møller算子实现的，该算子在我们称之为弱双曲的特定对称系统的$L^2$初始数据空间之间实现了酉同构，并与容许边界条件相耦合。特别地，我们证明对于带MIT边界条件的Dirac场，该同构可提升为Dirac场代数之间的$*$-同构，且任何Hadamard态均可沿此$*$-同构拉回，并保持其两点分布的奇性结构。
英文摘要：
The aim of this paper is to prove the existence of Hadamard states for Dirac fields coupled with MIT boundary conditions on any globally hyperbolic manifold with timelike boundary. This is achieved by introducing a geometric Møller operator which implements a unitary isomorphism between the spaces of $L^2$ -initial data of particular symmetric systems we call weakly-hyperbolic and which are coupled with admissible boundary conditions. In particular, we show that for Dirac fields with MIT boundary conditions, this isomorphism can be lifted to a $*$-isomorphism between the algebras of Dirac fields and that any Hadamard state can be pulled back along this $*$-isomorphism preserving the singular structure of its two-point distribution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
