Titlebook: Local Quantum Physics; Fields, Particles, A Rudolf Haag Textbook 19921st edition Springer-Verlag Berlin Heidelberg 1992 Algebraic field the

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Springer-Verlag Berlin Heidelberg 1992

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Local Quantum Physics978-3-642-97306-2Series ISSN 1864-5879 Series E-ISSN 1864-5887

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Von Neumann Algebras. C*-Algebras. W*-AlgebrasThe purpose of this section is to provide a brief glossary of mathematical terms, concepts and theorems which will be subsequently used. Proofs are only sketched or omitted altogether and the reader is referred to the bibliography at the end of the section to supplement this minimal exposition.

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The DHR-AnalysisAlthough, as mentioned, the DHR-criterion is too restrictive it is worthwhile to present the DHR-analysis. It illustrates the essential features. Modifications will be discussed in sections 3 and 5 of this chapter and, concerning infrared problems, in Chapter VI.

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Some Consequences of the Postulatesdomain and Λ any complex matrix satisfying (II.2.11) then .′., ? .′. with .′. = Λ. is in the analyticity domain and .(.′., ? .′.) may be found by applying (an extension of) the transformation law (II.1.9). Secondly in the complex Lorentz group the space-time reflection . → ? . can be connected by a continuous path to the identity.

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Theoretical and Mathematical Physicshttp://image.papertrans.cn/l/image/587701.jpg