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By definition, gauge theories - among the cornerstones of fundamental theoretical physics - involve more degrees of freedom than required by the underlying physics. The unphysical degrees of freedom must be shown not to yield unwarranted effects at every step in the formalism where explicit Lorentz covariance is required. The present work presents, in a rigorous way, a consistent formulation for the handling of noncovariant gauges in the quantization and renormalization of gauge theories. Though the path integral method is very convenient for the proof of unitarity and renormalizability of gauge theories, the canonical formalism is eventually necessary to expose the issues in a self-consistent way. These notes are written as an introduction to postgraduate students, lecturers and researchers in the field and assume prior knowledge of quantum field theory.

Gauge fields (Physics) --- Quantum field theory.

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The Transparent Becoming of World undertakes a penetrating inquiry into the quotidian world we take for granted and the brain that silently hoists our bubbles of world-thrownness. After critiquing the traditional views of direct realism, indirect realism and idealism, the continual becoming of world is explained by a novel integration of process dynamics, as formulated by Whitehead, Heidegger and Bohm, with the burgeoning field of quantum neurophilosophy. A rich ontological duality newly opened by quantum brain theory is exploited: the "between-two" of dual quantum modes. Existence as world-thrownness is between-two in waking and dreaming alike. This highly original interdisciplinary book may be of interest to philosophers, psychologists, neuroscientists, consciousness researchers, indeed anyone attracted to the enigma of their own lived existence. (Series A).

Mind and reality. --- Process philosophy. --- Quantum field theory. --- Neuropsychology --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Change --- Philosophy --- Reality and mind --- Reality --- Philosophy.

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For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics'.

Quantum field theory. --- Quantum field theory --- Atomic Physics --- Physics --- Physical Sciences & Mathematics --- Mathematical physics. --- Physical mathematics --- Relativistic quantum field theory --- Mathematics --- Physics. --- Quantum physics. --- Quantum Physics. --- Mathematical Methods in Physics. --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

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We are pleased by the positive resonance of our book which now necessitates a fourth edition. We have used this opportunity to implement corrections of misprints and amendments at several places, and to extend and improve the discussion of many of the exercises and examples. We hope that our presentation of the method of equivalent photons (Example 3. 17), the form factor of the electron (Example 5. 7), the infrared catastrophe (Example 5. 8) and the energy shift of atomic levels (Example 5. 9)arenow even better to understand. The new Exercise 5. 10 shows in detail how to arrive at the non-relativistic limit for the calculation of form factors. Moreover, we have brought up-to-date the Biographical Notes about physicists who have contributed to the dev- opment of quantum electrodynamics, and references to experimental tests of the t- ory. For example, there has been recent progress in the determination of the electric and magnetic form factors of the proton (discussed in Exercise 3. 5 on the Rosenbluth formula) and the Lamb shift of high-Z atoms (discussed in Example 5. 9 on the energy shift of atomic levels), while the experimental veri cation of the birefringence of the QED vacuum in a strong magnetic eld (Example 7. 8) remains unsettled and is a topic of active ongoing research.

Electronic books. -- local. --- Quantum electrodynamics -- Problems, exercises, etc. --- Quantum electrodynamics. --- Quantum electrodynamics --- Electricity & Magnetism --- Physics --- Physical Sciences & Mathematics --- Electrodynamics, Quantum --- QED (Physics) --- Physics. --- Quantum physics. --- Elementary particles (Physics). --- Quantum field theory. --- Quantum computers. --- Spintronics. --- Quantum Information Technology, Spintronics. --- Quantum Physics. --- Elementary Particles, Quantum Field Theory. --- Quantum field theory --- Schwinger action principle --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- deeltjes. --- computer techniques. --- computertechnieken. --- Computers --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Quantum electrodynamics - Problems, exercises, etc

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By definition, gauge theories - among the cornerstones of fundamental theoretical physics - involve more degrees of freedom than required by the underlying physics. The unphysical degrees of freedom must be shown not to yield unwarranted effects at every step in the formalism where explicit Lorentz covariance is required. The present work presents, in a rigorous way, a consistent formulation for the handling of noncovariant gauges in the quantization and renormalization of gauge theories. Though the path integral method is very convenient for the proof of unitarity and renormalizability of gauge theories, the canonical formalism is eventually necessary to expose the issues in a self-consistent way. These notes are written as an introduction to postgraduate students, lecturers and researchers in the field and assume prior knowledge of quantum field theory.

Physics. --- Elementary particles (Physics). --- Quantum field theory. --- Elementary Particles, Quantum Field Theory. --- Mathematical Methods in Physics. --- Gauge fields (Physics) --- Renormalization (Physics) --- Charge and mass renormalization --- Mass and charge renormalization --- Relativistic quantum field theory --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Electric charge and distribution --- Mass (Physics) --- Physical measurements --- Quantum field theory --- Group theory --- Symmetry (Physics) --- Quantum theory. --- Mathematical physics. --- Physical mathematics --- Physics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics