论文标题
洛伦兹歧管上的绿色双曲复合物
Green hyperbolic complexes on Lorentzian manifolds
论文作者
论文摘要
我们开发了称为绿色双曲线复合物的绿色双曲线算子的同源概括，涵盖了洛伦兹（Lorentzian）签名中量规理论二次作用功能的许多派生的关键基因座的例子。我们通过对迟滞和高级绿色的操作员的概括（称为智障和高级绿色的同型）来定义绿色双曲线复合体，这些操作员被证明是独特的，直到可缩度的选择空间。 We prove homological generalizations of the most relevant features of Green hyperbolic operators, namely that (1) the retarded-minus-advanced cochain map is a quasi-isomorphism, (2) a differential pairing (generalizing the usual fiber-wise metric) on a Green hyperbolic complex leads to covariant and fixed-time Poisson structures and (3) the retarded-minus-advanced cochain map is与这些泊松结构兼容，直到同型。
We develop a homological generalization of Green hyperbolic operators, called Green hyperbolic complexes, which cover many examples of derived critical loci for gauge-theoretic quadratic action functionals in Lorentzian signature. We define Green hyperbolic complexes through a generalization of retarded and advanced Green's operators, called retarded and advanced Green's homotopies, which are shown to be unique up to a contractible space of choices. We prove homological generalizations of the most relevant features of Green hyperbolic operators, namely that (1) the retarded-minus-advanced cochain map is a quasi-isomorphism, (2) a differential pairing (generalizing the usual fiber-wise metric) on a Green hyperbolic complex leads to covariant and fixed-time Poisson structures and (3) the retarded-minus-advanced cochain map is compatible with these Poisson structures up to homotopy.
