Non-perturbative Description of Quantum Systems
Non-perturbative Description of Quantum Systems

Author: Ilya Feranchuk

Publisher: Springer

Published: 2014-12-18

Total Pages: 374

ISBN-13: 3319130064

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This book introduces systematically the operator method for the solution of the Schrödinger equation. This method permits to describe the states of quantum systems in the entire range of parameters of Hamiltonian with a predefined accuracy. The operator method is unique compared with other non-perturbative methods due to its ability to deliver in zeroth approximation the uniformly suitable estimate for both ground and excited states of quantum system. The method has been generalized for the application to quantum statistics and quantum field theory. In this book, the numerous applications of operator method for various physical systems are demonstrated. Simple models are used to illustrate the basic principles of the method which are further used for the solution of complex problems of quantum theory for many-particle systems. The results obtained are supplemented by numerical calculations, presented as tables and figures.

Nonperturbative Quantum Field Theory
Nonperturbative Quantum Field Theory

Author: G. Hooft

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 603

ISBN-13: 1461307295

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During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.

tudes on Theoretical Physics
tudes on Theoretical Physics

Author: Leonid M. Barkovsky

Publisher: World Scientific

Published: 2004

Total Pages: 408

ISBN-13: 9789812702296

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- A collection of papers spanning decades and touching on a wide variety of research topics on modern theoretical physics written by leading scientists from the Belarusian State University bull; Provides concise information about the methods and applicati.

An Introduction to Non-Perturbative Foundations of Quantum Field Theory
An Introduction to Non-Perturbative Foundations of Quantum Field Theory

Author: Franco Strocchi

Publisher: Oxford University Press, USA

Published: 2013-02-14

Total Pages: 270

ISBN-13: 0199671575

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The book discusses fundamental aspects of Quantum Field Theory and of Gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum Chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.

Lectures on Non-perturbative Canonical Gravity
Lectures on Non-perturbative Canonical Gravity

Author: Abhay Ashtekar

Publisher: World Scientific

Published: 1991

Total Pages: 356

ISBN-13: 9810205740

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Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up- to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.

Quantum Systems: New Trends And Methods - Proceedings Of The International Workshop
Quantum Systems: New Trends And Methods - Proceedings Of The International Workshop

Author: Asim Orhan Barut

Publisher: World Scientific

Published: 1995-02-21

Total Pages: 422

ISBN-13: 981454986X

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Quantum systems in all areas of physics, from atomic and molecular physics, nuclear and particle physics to condensed matter and astrophysics, provide a rich mosaic of different structures. Yet there are some simple and universal working principles of nature which seem to govern these structures and manifest themselves in various forms, as well as likely hypothetical ones which might do the same. For example, the same symmetry group structure occurs again and again in optics, atomic physics and particle physics. Concepts like potential, phases, bound states, tunneling, interference, solitons, radiation and resonance are universal.It is for those reasons that a collection of recent works in the many areas of physics on quantum structures and the methods for their investigation is important. The present volume fulfills this task to a large extent. The contributions are wide-ranging and yet there is a certain continuity. The main topics, namely non-perturbative methods in quantum theory, quantum nonlinear systems, quantum phases and magnetic monopoles, are covered by longer review articles and are enriched by many related contributions. It is also very appropriate that the corresponding mathematical methods, such as those for solving Schrödinger and relativistic wave equations, as well as those of algebra and group representations and analysis, are included in this volume.

Quantum Chromodynamics
Quantum Chromodynamics

Author: B. L. Ioffe

Publisher: Cambridge University Press

Published: 2010-01-21

Total Pages: 597

ISBN-13: 0521631483

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Aimed at graduate students and researchers in theoretical physics, this book presents the modern theory of strong interaction: quantum chromodynamics (QCD). The book exposes various perturbative and nonperturbative approaches to the theory, including chiral effective theory, the problems of anomalies, vacuum tunnel transitions, and the problem of divergence of the perturbative series. The QCD sum rules approach is exposed in detail. A great variety of hadronic properties (masses of mesons and baryons, magnetic moments, form factors, quark distributions in hadrons, etc.) have been found using this method. The evolution of hadronic structure functions is presented in detail, together with polarization phenomena. The problem of jets in QCD is treated through theoretical description and experimental observation. The connection with Regge theory is emphasized. The book covers many aspects of theory which are not discussed in other books, such as CET, QCD sum rules, and BFKL. • Provides a deep understanding of various aspects of the modern theory of strong interaction • Presents the general properties of QCD, before exploring perturbative and nonperturbative approaches • Discusses aspects of the theory such as CET, QCD sum rules, and BFKL, which are not covered in other books

Non-Perturbative Field Theory
Non-Perturbative Field Theory

Author: Yitzhak Frishman

Publisher: Cambridge University Press

Published: 2010-04-08

Total Pages: 455

ISBN-13: 1139486489

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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.

Non-perturbative Renormalization
Non-perturbative Renormalization

Author: Vieri Mastropietro

Publisher: World Scientific

Published: 2008

Total Pages: 303

ISBN-13: 9812792392

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The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providing a mathematical construction of models at low dimensions and discussing the removal of the ultraviolet and infrared cut-off, the verification of the axioms and the validity of Ward Identities with the relative anomalies. The second part is devoted to lattice 2D Statistical Physics, analyzing in particular the theory of universality in perturbed Ising models and the computation of the non-universal critical indices in Vertex or Ashkin-Teller models. Finally the third part is devoted to the analysis of complex quantum fluids showing Luttinger of Fermi liquid behavior, like the 1D or 2D Hubbard model.