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Quantum Field Theory
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Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. Since the very beginning of western philosophy reflections about the material world which go beyond the directly observable play a central role in philosophy. Starting with the presocratics it has always been a point of debate what the fundamental characteristics of the material world are. Is everything constantly changing or are there certain permanent features? What is basic and what is merely a matter of perspective and appearance? In the course of time various answers have been given and conflicting views have often been alternating in their predominance.
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Quantum Field Theory-1 is the first course in a three course sequence which provides an introduction to quantum field theory. Topics covered in QFT-1 include: Lagrangian field theory, symmetries and conservation laws, including global and local (gauge) continuous symmetries, Noether's theorem, and the Lorentz group. Relativistic wave equations including the Klein-Gordon equation, the Dirac equation, and electromagnetism. Canonical quantization of fields, interacting fields, Feynman rules and diagrams, the S-Matrix, cross sections and decay rates, and elementary processes from quantum electrodynamics.
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Quantum Field Theory is designed as a short and simple introduction for students beginning research in theoretical and experimental physics. The three main objectives are to explain the basic physics and formalism of quantum field theory, to make the reader fully proficient in perturbation theory calculations using Feynman diagrams, and to introduce the reader to gauge theories, which play such a central role in elementary particle physics. The theory is applied first to Quantum Electrodynamics(QED) and then to the unified theory of weak and electromagnetic interactions. After studying this book, the reader should be able to calculate any process in lowest order perturbation theory for both QED and the unified electroweak theory, and in addition, calculate lowest order radiative corrections in QED using the powerful tecnique of dimensional regularisation. The Revised Edition brings the book fully up to date and makes some improvements in the treatment of dimensional regularization.
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Quantum field theory started with a theoretical framework that was built in analogy to quantum mechanics. Although there was no unique and fully developed theory, quantum field theoretical tools could be applied to concrete processes. Examples are the scattering of radiation by free electrons (“Compton scattering”), the collision between relativistic electrons or the production of electron-positron pairs by photons. Calculations to the first order of approximation were quite successful, but most people working in the field thought that QFT still had to undergo a major change. On the one side some calculations of effects for cosmic rays clearly differed from measurements. On the other side and, from a theoretical point of view more threatening, calculations of higher orders of the perturbation series led to infinite results.
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Quantum electrodynamics, commonly referred to as QED, is a quantum field theory of the electromagnetic force. Taking the example of the force between two electrons, the classical theory of electromagnetism would describe it as arising from the electric field produced by each electron at the position of the other. The force can be calculated from Coulomb's law.
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Quantum fields are well-known to violate all the pointwise energy conditions of classical general relativity. This talk will review the subject of quantum energy inequalities, which are constraints satisfied by weighted averages of the stress-energy tensor and which may be regarded as the vestiges of the classical energy conditions after quantisation.
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Quantum Field Theory