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| Author | : Arianna Toniato |
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| Release | : 2018 |
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| Author | : Yochai Ben-Horin |
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| Total Pages | : 250 |
| Release | : 1997 |
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| Author | : G. 't Hooft |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 437 |
| Release | : 2013-03-09 |
| Genre | : Science |
| ISBN | : 1468475711 |
Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a non-perturbative understanding of gauge theories. This phase has so far been marked by the introduc tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these non-perturbative, global aspects of non-abelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics.
| Author | : Rajsekhar Bhattacharyya |
| Publisher | : LAP Lambert Academic Publishing |
| Total Pages | : 124 |
| Release | : 2011-07 |
| Genre | : |
| ISBN | : 9783845412207 |
Studying dualities in gauge theory we develop a new formalism which assumes the Lagrangian density, and hence also the action, depends explicitly on space-time. We first develop our formalism to study electro-magnetic duality. Starting from Lagrangian field theory and the variational principle, we show that duality in the equations of motion can also be obtained by introducing explicit spacetime dependence into the Lagrangian. Poincare invariance is achieved precisely when the duality conditions are satisfied, in a particular way. The analysis and resulting criteria, are valid for both Abelian and non-Abelian dualities. We illustrate how the Dirac string solution, Dirac quantisation condition, t'Hooft-Polyakov monopole solutions are recovered, and further show that a systematic procedure emerges for obtaining new classical solutions of Yang-Mills theory. Moreover, these results occur in a way that is strongly reminiscent of the holographic principle. We use our formalism to study weak-strong duality in the equivalence of the Sine Gordon-Massive Thirring models. Further we apply the formalism to the action relevant for general relativity to obtain a Barriola-Vilenkin type solution.
| Author | : Yitzhak Frishman |
| Publisher | : Cambridge University Press |
| Total Pages | : 455 |
| Release | : 2010-04-08 |
| Genre | : Science |
| ISBN | : 1139486489 |
Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.
| Author | : Luciano Maiani |
| Publisher | : |
| Total Pages | : 276 |
| Release | : 1992 |
| Genre | : Chirality |
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| Author | : John M. Cornwall |
| Publisher | : Cambridge University Press |
| Total Pages | : 305 |
| Release | : 2010-12-23 |
| Genre | : Science |
| ISBN | : 1139494279 |
Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon mass arises in QCD. Applications are given to the center vortex picture of confinement, the gauge-invariant treatment of resonant amplitudes, the definition of non-Abelian effective charges, high-temperature effects, and even supersymmetry. This book is ideal for elementary particle theorists and graduate students.
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| Total Pages | : 0 |
| Release | : 1988 |
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| Author | : Urko Reinosa |
| Publisher | : Springer Nature |
| Total Pages | : 280 |
| Release | : 2022-11-17 |
| Genre | : Science |
| ISBN | : 3031113756 |
This book offers an original view of the color confinement/deconfinement transition that occurs in non-abelian gauge theories at high temperature and/or densities. It is grounded on the fact that the standard Faddeev-Popov gauge-fixing procedure in the Landau gauge is incomplete. The proper analysis of the low energy properties of non-abelian theories in this gauge requires, therefore, the extension of the gauge-fixing procedure, beyond the Faddeev-Popov recipe. The author reviews various applications of one such extension, based on the Curci-Ferrari model, with a special focus on the confinement/deconfinement transition, first in the case of pure Yang-Mills theory, and then, in a formal regime of Quantum Chromodynamics where all quarks are considered heavy. He shows that most qualitative aspects and also many quantitative features of the deconfinement transition can be accounted for within the model, with only one additional parameter. Moreover, these features emerge in a systematic and controlled perturbative expansion, as opposed to what would happen in a perturbative expansion within the Faddeev-Popov model. The book is also intended as a thorough and pedagogical introduction to background field gauge techniques at finite temperature and/or density. In particular, it offers a new and promising view on the way these techniques might be applied at finite temperature. The material aims at graduate students or researchers who wish to deepen their understanding of the confinement/deconfinement transition from an analytical perspective. Basic knowledge of gauge theories at finite temperature is required, although the text is designed in a self-contained manner, with most concepts and tools introduced when needed. At the end of each chapter, a series of exercises is proposed to master the subject.
