Titlebook: Quantum Field Theory; Competitive Models Bertfried Fauser,Jürgen Tolksdorf,Eberhard Zeidler Book 2009 Birkhäuser Basel 2009 Feynmann path i

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Noncommutative Field Theories from a Deformation Point of View,ver the classical space-time. For gauge theories we establish a notion of deformation quantization of a principal fibre bundle and show how the deformation of associated vector bundles can be obtained.

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The Structure of Green Functions in Quantum Field Theory with a General State,e complex than in the vacuum, because they cannot be written in terms of standard Feynman diagrams. Here a method is proposed to determine the structure of these Green functions and to derive nonperturbative equations for them. The main idea is to transform the cumulants describing correlations into interaction terms.

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,Topos Theory and ‘Neo-Realist’ Quantum Theory,a brief introduction to this approach, emphasizing the logical aspects. Each topos serves as a ‘mathematical universe’ with an internal logic, which is used to assign truth-values to all propositions about a physical system. We show in detail how this works for (algebraic) quantum theory.

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