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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Basic Strategies in Quantum Field Theorys that are related to the outcome of physical experiments. It is then the hard task of mathematicians to give rigorous proofs for the heuristic arguments of physicists. The flow of ideas from physics to mathematics is an indispensable source of inspiration for mathematicians.

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The Operator Approachules for Feynman diagrams and the representation of propagators by functional integrals. Typically, this approach does not use operators in Hilbert spaces, that is, the methods of functional analysis do not play any role. Historically, in the 1920s quantum mechanics was first based on operator theor

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Peculiarities of Gauge Theoriestypical difficulty is that the original response equations are not uniquely solvable because of the local gauge invariance. . This leads to additional terms in the Lagrangian density which enter the response equations. This is called gauge fixing. The response equations depend on the gauge fixing. W

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ial: 1 Daß ich erkenne, was die Welt im Innersten zusammenh¨ alt. Faust Concepts without intuition are empty, intuition without concepts is blind. Immanuel Kant (1724–1804) The greatest mathematicians like Archimedes, Newton, and Gauss have always been able to combine theory and applications into on

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Historical Introductionells us the following: . More precisely, the action is critical. This means that the first variation of the action . vanishes, .=0. In 1918 Emmy Noether (1882–1935) proved a fundamental mathematical theorem. The famous Noether theorem tells us that

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Phenomenology of the Standard Model for Elementary Particlesd the textbooks by Nachtmann (1990), Coughlan and Dood (1991), Sibold (2001), and Seiden (2005). For the history of elementary particle physics, see the beautiful books by the two Nobel laureates Steven Weinberg (1983), (1995) and Martinus Veltman (2003).

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Many-Particle Systems in Mathematics and Physicsly different approaches can be traced back to the same mathematical root, namely, the notion of partition function. In modern quantum field theory, the Feynman functional integral can be viewed as a partition function, as we will discuss later on. The typical procedure proceeds in the following two steps.