Pfaffians on Hilbert space
Pfaffians on Hilbert space
复制标题
希尔伯特空间上的普法夫式
DOI：
10.1016/0022-1236(89)90024-4
复制
发表时间：
1989
影响因子：
1.7
通讯作者：
J. Weitsman
中科院分区：
文献类型：
--
作者：
A. Jaffe;A. Leśniewski;J. Weitsman
将行列式理论推广到无限维空间上的算子是分析的基石。由Fredholm和其他人发展的这个理论允许对K定义det（Z+ K），K是第一个Schatten类I的元素，[1，6，？]。类似的，正则化的行列式det，（Z+ K）存在K Ez，。在实际应用中，算子Z+ K往往是两个无界算子之比，如两个拉普拉斯或Dirac算子.本文研究了Pfizer算子的类似结构.在有限维情况下，普法希安是众所周知的反对称矩阵的行列式的平方根。事实证明，无限维Pfweian的概念在各种应用中自然出现，例如，环群的表示理论[S]，共形场论[8]和与iV= 1超对称性相关的环空间指数定理[3]。我们提出了一个系统的治疗的存在性和连续性的Pfaflians在无限维。对于A，BE Z，我们定义相对Pfafian Pf（A，B），在有限维中并且当A可逆时，其等于
The generalization of the theory of determinants to operators on infmitedimensional spaces is a cornerstone of analysis. This theory, developed by Fredholm and others, allows the definition of det (Z+ K) for K an element of the first Schatten class I,[l, 6,?]. Analogous, regularized determinants det,(Z+ K) exist for K EZ,. In the applications, the operator Z+ K is often the ratio of two unbounded operators, eg, two Laplace or Dirac operators.In this paper we investigate analoguous structures for the Pfaffian. In the finite-dimensional case, the Pfahian is well known as a square root of the determinant of an antisymmetric matrix. It turns out that the notion of an infinite-dimensional Pfaffian emerges naturally in various applications, eg, representation theory of loop groups [S], conformal field theory [8], and loop space index theorems related to iV= 1 supersymmetry [3]. We present a systematic treatment of the existence and continuity of Pfaflians in infinite dimensions. For A, BE Z, we define the relative Pfafian Pf (A, B), which in finite dimensions and when A is invertible equals