论文标题
雷格恩场理论中一些非正常运算符的光谱分析
Spectral analysis of some non-normal operators arising in Reggeon field theory
论文作者
论文摘要
在这项工作中，我们介绍了Reggeon Field理论中出现的非正常运算符家族的完整光谱研究。这个操作员家族是一个原始的例子，使我们能够发现最新的时空反射对称性（PT对称性）的物理要求理论，而不会失去量子力学的任何基本物理特征[Bender]。 Reggeon野外理论的早期研究在1970年代后期，许多研究者观察到模型的立方量子力学的哈密顿量可能具有真正的特征值[Bower等]。对这个运营商家族的研究，允许我们发现光谱理论和功能分析的一些良好结果，尤其是与数学物理问题基本解决方案完整相关的结果。我们使用一个复杂变量的全态函数的知识基础和希尔伯特空间的性质。在这项工作中，需要光谱理论的知识和标准水平的功能分析（请参阅[Kato]，[Ghohberg2等]和[Markus]）。还要求知道半群理论的基本属性，例如（[Pazy]）。
In this work, we present a complete spectral study of a family of non-normal operators arising in Reggeon field theory. This family of operators is an original example who permit us to discover the recent theory of physical requirement of space-time reflection symmetry (PT symmetry) without losing any of the essential physical features of quantum mechanics [Bender]. Early studies of Reggeon field theory, in the late 1970s led a number of investigators to observe that model cubic quantum-mechanical Hamiltonians might have real eigenvalues [Bower et al]. The study of this family of operators, permit us to discover some fine results of Spectral Theory and Functional Analysis in particular the results connected with completeness of elementary solutions of mathematical physics problems. We use knowledge basics of holomorphic functions of one complex variable and the properties of Hilbert spaces. In this work the knowledge of spectral theory and the functional analysis of standard level is required (see [Kato], [Ghohberg2 et al] and [Markus]). It is also requested to know the basic properties of semigroup theory see for example ([Pazy]).
