| 期刊全称 | Beyond Partial Differential Equations | | 期刊简称 | On Linear and Quasi- | | 影响因子2023 | Horst Reinhard Beyer | | 视频video | | | 发行地址 | Includes supplementary material: | | 学科分类 | Lecture Notes in Mathematics | | 图书封面 |  | | 影响因子 | Semigroup Theory uses abstract methods of Operator Theory to treat initial bou- ary value problems for linear and nonlinear equations that describe the evolution of a system. Due to the generality of its methods, the class of systems that can be treated in this way exceeds by far those described by equations containing only local op- ators induced by partial derivatives, i.e., PDEs. In particular, that class includes the systems of Quantum Theory. Another important application of semigroup methods is in ?eld quantization. Simple examples are given by the cases of free ?elds in Minkowski spacetime like Klein-Gordon ?elds, the Dirac ?eld and the Maxwell ?eld, whose ?eld equations are given by systems of linear PDEs. The second quantization of such a ?eld replaces the ?eld equation by a Schrodinger ¨ equation whose Hamilton operator is given by the second quantization of a non-local function of a self-adjoint linear operator. That operator generates the semigroup given by the time-development of the solutions of the ?eld equation corresponding to arbitrary initial data as a function of time. | | Pindex | Book 2007 |
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发表于 2025-3-21 16:42:34
