Beyond Partial Differential Equations

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 304 pp. Englisch.

Bestandsnummer des Verkäufers 9783540711285

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Bibliografische Details

Titel

Beyond Partial Differential Equations

Verlag

Springer Berlin Heidelberg, Springer Berlin Heidelberg Apr 2007

Erscheinungsjahr

2007

Sprache

Englisch

ISBN-10

3540711287

ISBN-13

9783540711285

Einband

Taschenbuch

Zustand

Neu

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