Statistical Approach to Quantum Field Theory PDF Download
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Author: Andreas Wipf
Publisher: Springer Nature
ISBN: 3030832635
Category : Science
Languages : en
Pages : 568
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Book Description
This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Author: Andreas Wipf
Publisher: Springer Nature
ISBN: 3030832635
Category : Science
Languages : en
Pages : 568
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Book Description
This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Author: Norman J. M. Horing
Publisher: Oxford University Press
ISBN: 0198791941
Category : Science
Languages : en
Pages : 453
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Book Description
The methods of coupled quantum field theory, which have played a major role in the extensive development of nonrelativistic quantum many-particle theory and condensed matter physics, are at the core of this book.
Author: G. Mussardo
Publisher: Oxford University Press, USA
ISBN: 0199547580
Category : Mathematics
Languages : en
Pages : 778
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Book Description
A thorough and pedagogical introduction to phase transitions and exactly solved models in statistical physics and quantum field theory.
Author: James Glimm
Publisher: Springer Science & Business Media
ISBN: 9780817632755
Category : Science
Languages : en
Pages : 430
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Book Description
This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and Yang-Mills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anti-commute in the case of fer mions) at space-like separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields.
Author: Michel Le Bellac
Publisher:
ISBN: 9787515804156
Category :
Languages : en
Pages : 7
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Book Description
Author: Dr. Gérard G. Emch
Publisher: Courier Corporation
ISBN: 0486151719
Category : Science
Languages : en
Pages : 336
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Book Description
This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.
Author: Alekseĭ Alekseevich Abrikosov
Publisher:
ISBN:
Category : Low temperature research
Languages : en
Pages : 376
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Book Description
Author: Claude Itzykson
Publisher: Cambridge University Press
ISBN: 9780521408059
Category : Science
Languages : en
Pages : 440
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Book Description
Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.
Author: Jan Ambjørn
Publisher: Cambridge University Press
ISBN: 0521461677
Category : Science
Languages : en
Pages : 377
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Book Description
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.
Author: A.N. Vasiliev
Publisher: CRC Press
ISBN: 9789056990350
Category : Science
Languages : en
Pages : 336
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Book Description
Providing a systematic introduction to the techniques which are fundamental to quantum field theory, this book pays special attention to the use of these techniques in a wide variety of areas, including ordinary quantum mechanics, quantum mechanics in the second-quantized formulation, relativistic quantum field theory, Euclidean field theory, quantum statistics at finite temperature, and the classical statistics of nonideal gas and spin systems. The extended chapter on variational methods and functional Legendre transformations contains completely original material.
