论文标题
Minkowski空间中的因果关系系统的本地代数
Local Algebras for Causal Fermion Systems in Minkowski Space
论文作者
论文摘要
在因果费系统理论中介绍了局部代数的概念。在Minkowski空间中的正规迪拉克海真空吸尘器的示例中，研究了它们的特性。解决了换向关系，并讨论了规范换向关系的差异。结果表明，与库奇表面相关的时空点算子满足时间切片公理。事实证明，由于Hegerfeldt的定理，操作员在开放式设置中产生的代数是不可约的。通过分析删除正则化时，通过分析代数中的运算符的期望值来恢复光锥结构。结果表明，每个时空操作员都会以远离其空锥的代数为通勤，直至涉及正则化长度的小校正。
A notion of local algebras is introduced in the theory of causal fermion systems. Their properties are studied in the example of the regularized Dirac sea vacuum in Minkowski space. The commutation relations are worked out, and the differences to the canonical commutation relations are discussed. It is shown that the spacetime point operators associated to a Cauchy surface satisfy a time slice axiom. It is proven that the algebra generated by operators in an open set is irreducible as a consequence of Hegerfeldt's theorem. The light cone structure is recovered by analyzing expectation values of the operators in the algebra in the limit when the regularization is removed. It is shown that every spacetime point operator commutes with the algebras localized away from its null cone, up to small corrections involving the regularization length.
