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Quantum field theory (QFT) is the application of quantum mechanics to fields. It provides a theoretical framework, widely used in particle physics and condensed matter physics, in which to formulate consistent quantum theories of many-particle systems, especially in situations where particles may be created and destroyed. Non-relativistic quantum field theories are needed in condensed matter physics— for example in the BCS theory of superconductivity. Relativistic quantum field theories are indispensable in particle physics (see the standard model), although they are known to arise as effective field theories in condensed matter physics.
Origin
Quantum field theory originated in the problem of computing the energy radiated by an atom when it dropped from one quantum state to another of lower energy. This problem was first examined by Max Born and Pascual Jordan in 1925. In 1926, Max Born, Werner Heisenberg and Pascual Jordan wrote down the quantum theory of the electromagnetic field neglecting polarization and sources to obtain what would today be called a free field theory. In order to quantize this theory, they used the canonical quantization procedure. In 1927, Paul Dirac gave the first consistent treatment of this problem. Quantum field theory followed unavoidably from a quantum treatment of the only known classical field, ie, electromagnetism. The theory was required by the need to treat a situation where the number of particles changes. Here, one atom in the initial state becomes an atom and a photon in the final state.
It was obvious from the beginning that the quantum treatment of the electromagnetic field required a proper treatment of relativity. Jordan and Wolfgang Pauli showed in 1928 that commutators of the field were actually Lorentz invariant. By 1933, Niels Bohr and Leon Rosenfeld had related these commutation relations to a limitation on the ability to measure fields at space-like separation. The development of the Dirac equation and the hole theory drove quantum field theory to explain these using the ideas of causality in relativity, work that was completed by Wendell Furry and Robert Oppenheimer using methods developed for this purpose by Vladimir Fock. This need to put together relativity and quantum mechanics was a second motivation which drove the development of quantum field theory. This thread was crucial to the eventual development of particle physics and the modern (partially) unified theory of forces called the standard model.
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Adiabatically switched-on electrical bias and the Landauer--B[u-umlaut]ttiker formula
H. D. Cornean, P. Duclos, G. Nenciu, and R. Purice Consider a three dimensional system which looks like a cross connected pipe system, i.e., a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we adiabatically turn on an electrical bias between leads. The mai ... [J. Math. Phys. 49, 102106 (2008)] published Fri Oct 10, 2008.
Lower spectral branches of a spin-boson model
Nicolae Angelescu, Robert A. Minlos, Jean Ruiz, and Valentin A. Zagrebnov We study the structure of the spectrum of a two-level quantum system weakly coupled to a boson field (spin-boson model). Our analysis allows to avoid the cutoff in the number of bosons, if their spectrum is bounded below by a positive constant. We show that, for small coupling constant, the lower pa ... [J. Math. Phys. 49, 102105 (2008)] published Fri Oct 10, 2008.
The structure of degradable quantum channels
Toby S. Cubitt, Mary Beth Ruskai, and Graeme Smith Degradable quantum channels are among the only channels whose quantum and private classical capacities are known. As such, determining the structure of these channels is a pressing open question in quantum information theory. We give a comprehensive review of what is currently known about the struct ... [J. Math. Phys. 49, 102104 (2008)] published Wed Oct 8, 2008.
Net Advance in Physics - Quantum Field Theory -
Development - Research and Development in Vacuum Fluctuations, Casimir Forces and EPR Entangled States
Meta Description: [ Leaders in Breakthrough Technology, Quantum Fields Contract Research, Development, Consulting, Nanotechnology Instruments ]
A Short Introduction to Non-Relativistic Effective Field Theories - A discussion of effective field theories for heavy bound systems, particularly bound systems involving two heavy quarks.
Algebraic Quantum Field Theory - A collection of resources for algebraic quantum field theory
An Introduction to Pomerons - Talk given at Workshop on Diffractive Physics
Casimir Effect: Physical Manifestations of Zero-Point Energy - Zero-point fluctuations in quantum fields give rise to observable forces between material bodies, the so-called Casimir forces.These lectures present the theory of the Casimir effect, primarily formulated in terms of Green's functions.
Chern-Simons Theory - A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented.
Eurotraps - A European experiment intended to test the theory of quantum electrodynamics to extremely high accuracy.
Evolution of the Bogoluibov Renormalization Group - A simple introduction into the renormalization group (RG) in quantum field theory and an overview of the renormalization group method. The third section is devoted to essential topics of the renorm-group use in the QFT.
Feynman Diagrams - A summary of the rules governing the creation of Feynman diagrams.
Goldstone Bosons - These notes review the effective lagrangian treatment of Goldstone and pseudo-Goldstone bosons, taking examples from high-energy/nuclear and condensed-matter physics.
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Introduction to Gauge Theories - These lectures present an elementary introduction to quantum gauge fields.
Introduction to Seiberg-Witten Theory - An elementary introduction to the recent solution of supersymmetric Yang-Mills theory. In addition, review of how it can be re-derived from string duality.
New Developments in the Casimir Effect - A review of both new experimental and theoretical developments in the Casimir effect. [Postscript PDF format]
Noether's Theorem in a Nutshell - An overview of Noether's theorem
Notes on Seiberg-Witten Gauge Theory - These notes provide an introductory exposition of the Seiberg-Witten gauge theory.
Quantum Field Theory in Curved Spacetime - These postscript lectures deal with selected aspects of quantum field theory in curved spacetime
Quantum Fields Near Black Holes - This review gives an introduction into problems, concepts and techniques when quantizing matter fields near black holes. The first part focusses on quantum fields in general curved space-times. The second part is devoted to a detailed treatment of the Unruh effect in uniformly accelerated frames and the Hawking radiation of black holes
Renormalization Made Easy - A non-technical introduction to the renormalization of quantum field theories.
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Some Articles of Proceedings of International Colloquium on Moden Quantum Field Theory, 1994, TIFR - Copies of these articles in TeX and postscript formats.
Technicolor 2000 - This review is based on lectures on technicolor and extended technicolor presented at the Frascati Spring School in May 2000
The Casimir Effect - What is the Casimir Effect? From the Usenet FAQ.
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The State of Matrix Theory - A set of lecture notes with RealPlayer audio on Matrix Theory
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Topics in Nonequilibrium Field Theory - Nonequilibrium field theory covers a variety of topics such as transport theory of quantum fields, nonequilibrium phase transitions, the nucleation and transport of topological defects and other nonlinear coherent structures, as well as fundamental issues such as the quantum-classical transition and the coherent control of quantum systems.
Topics in Quantum Field Theory - Several files in LaTeX format cover selected topics in Quantum Field Theory and Integrable Systems
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What are C* Algebras Good For? - An introduction to C* Algebras and their applications in field theory.
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