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Statistical Approach to Quantum Field Theory

Author : Andreas Wipf

Publisher : Springer Nature

Page : 568 pages

File Size : 15,85 MB

Release : 2021-10-25

Category : Science

ISBN : 3030832635

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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.



Quantum Field Theory and Statistical Mechanics

Author : James Glimm

Publisher : Springer Science & Business Media

Page : 430 pages

File Size : 21,36 MB

Release : 1985-01-01

Category : Science

ISBN : 9780817632755

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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.



Algebraic Methods in Statistical Mechanics and Quantum Field Theory

Author : Dr. Gérard G. Emch

Publisher : Courier Corporation

Page : 336 pages

File Size : 26,20 MB

Release : 2014-08-04

Category : Science

ISBN : 0486151719

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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.



Statistical Field Theory

Author : G. Mussardo

Publisher : Oxford University Press, USA

Page : 778 pages

File Size : 35,53 MB

Release : 2010

Category : Mathematics

ISBN : 0199547580

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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.







Functional Methods in Quantum Field Theory and Statistical Physics

Author : A.N. Vasiliev

Publisher : CRC Press

Page : 336 pages

File Size : 13,74 MB

Release : 1998-07-28

Category : Science

ISBN : 9789056990350

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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.



Statistical Physics of Fields

Author : Mehran Kardar

Publisher : Cambridge University Press

Page : 376 pages

File Size : 34,38 MB

Release : 2007-06-07

Category : Science

ISBN : 1139855883

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Book Description

While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underlie the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.





Elements of Statistical Mechanics

Author : Ivo Sachs

Publisher : Cambridge University Press

Page : 0 pages

File Size : 17,59 MB

Release : 2010-06-10

Category : Science

ISBN : 9780521143646

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Book Description

This concise introduction to the key concepts and tools of modern statistical mechanics is self-contained. Combining analytical and numerical techniques, it also covers advanced topics such as non-relativistic quantum field theory. After introducing classical analytical techniques, the authors present important numerical methods and a diverse range of applications. Quantum statistical mechanics is then analyzed and applied to topics in astrophysics and cosmology. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced students in physics, chemistry and mathematics.