Titlebook: Quantum Field Theory I: Basics in Mathematics and Physics; A Bridge between Mat Eberhard Zeidler Book 20061st edition Springer-Verlag Berli

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Analyticityrespectively. The set of all complex numbers is denoted by ?; it is also called the complex plane. Using polar coordinates, each complex number .=.+. can be written uniquely as . where . The real numbers . are called the modulus and the principal argument of ., respectively (Fig. 4.1). Using the Eul

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A Glance at Topologyo topology: . Topology was created by Poincaré (1854–1912) at the end of the 19th century and was motivated by the investigation of Riemann surfaces and the qualitative behavior of the orbits of planets, asteroids, and comets in celestial mechanics. Topology studies far-reaching generalizations of t

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Rigorous Finite-Dimensional Magic Formulas of Quantum Field Theoryed by physicists. Mathematicians should note that we introduce two crucial tools which are not mentioned in the standard literature on finite-dimensional linear algebra, namely, . These tools are also very useful for mathematics itself.

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Rigorous Finite-Dimensional Perturbation Theorys to replace the original problem by an equivalent one by introducing so-called regularizing terms. We have to distinguish between . In celestial mechanics, it is well-known that resonance may cause highly complicated motions of asteroids. . In Sect.?7.16, the non-resonance case and the resonance ca

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Fermions and the Calculus for Grassmann Variables-integer spin like electrons and quarks). The rigorous finite-dimensional approach from the preceding Chap.?7 refers to bosons. However, it is possible to extend this approach to fermions by replacing complex numbers by Grassmann variables. In this chapter, we are going to discuss this.

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