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  3. Quantum Field Theory and Condensed Matter
  • Cited by 51
Publisher:
Cambridge University Press
Online publication date:
October 2017
Print publication year:
2017
Online ISBN:
9781139044349
DOI:
https://doi.org/10.1017/9781139044349
Subjects:
Physics and Astronomy, Condensed Matter Physics, Nanoscience and Mesoscopic Physics, Theoretical Physics and Mathematical Physics
Information

Book description

Providing a broad review of many techniques and their application to condensed matter systems, this book begins with a review of thermodynamics and statistical mechanics, before moving onto real and imaginary time path integrals and the link between Euclidean quantum mechanics and statistical mechanics. A detailed study of the Ising, gauge-Ising and XY models is included. The renormalization group is developed and applied to critical phenomena, Fermi liquid theory and the renormalization of field theories. Next, the book explores bosonization and its applications to one-dimensional fermionic systems and the correlation functions of homogeneous and random-bond Ising models. It concludes with Bohm–Pines and Chern–Simons theories applied to the quantum Hall effect.  Introducing the reader to a variety of techniques, it opens up vast areas of condensed matter theory for both graduate students and researchers in theoretical, statistical and condensed matter physics.

Awards

Honourable mention, 2018 PROSE Award for Chemistry and Physics

Reviews

'The study of minimally complicated models is … central to the field of condensed-matter physics. Those models, and the tools needed to understand them, are the subject of Ramamurti Shankar’s new book, Quantum Field Theory and Condensed Matter: An Introduction. What is different about Shankar’s text? For one thing, it is shorter [than his competitors]. Accordingly, Shankar’s book is less ambitious in its aim and more selective in its content. That makes it both a more introductory text and a friendlier read. It will be a good textbook for a one-semester first-year graduate course.'

Mike Stone Source: Physics Today

'[The book] provides a broad review of many different techniques and models used daily in the theoretical condensed matter community. The presentation is done in a quite individual and elegant way … the book can be used self-consistently as a source for an advanced statistical mechanics course at the master degree level … Shankar covers a wide variety of models ranging from the celebrated classical two-dimensional Ising model … to the XY model and Zq gauge theories, and finally to models developed for the quantum Hall effect such as the Bohm–Pines or Chern–Simons theories. In the middle of the book, there are six chapters giving an extensive survey on the renormalization group theory (a book within a book, as Daniel Arovas wrote) and two self-contained chapters dealing with bosonization. Again, here, these chapters may be used self-consistently in order to teach the material.'

Source: Acta Crystallographica Section A: Foundations Advances

'Since the Nobel Prize-winning work of Ken Wilson in the 1970s, quantum field theory has been a fundamental tool in condensed matter theory … Shankar presents more than enough material for a one- or two-semester course, and the book could be used to teach at a variety of levels. There is a substantial amount of classic material: the Ising model and critical phenomena, the relation of the Feynman path integral to statistical mechanics, and the renormalization group. The text ventures beyond these, with treatments of coherent state path integrals, gauge theories, duality, and bosonization. Topics of great modern importance include Majorana fermions and the quantum Hall effect. It is notable that both the Lagrangian and Hamiltonian forms of lattice models are treated. This clear, authoritative text should be available at any institution where modern condensed matter physics is studied.'

M. C. Ogilvie Source: Choice

'… the first few chapters are about techniques one has to learn before learning the real techniques. The book starts with a review of Thermodynamics and Statistical Mechanics. The Ising model is discussed next. … [Other] topics covered are Statistical to Quantum Mechanics … Quantum to Statistical Mechanics … Feynman Path Integral, Coherent State Path Integrals, Two dimensional Ising model and its exact solution and Majorana Fermions. Further Gauge Theories, The Renormalization Group and Critical Phenomena, different views of Renormalization, Bosonization and Duality and Triality are described. The final Chapter covers Techniques for Quantum Hall Effect. Each chapter ends with a list of references for further reading. Overall, a very useful book for researchers.'

T. C. Mohan Source: zbMATH

'The next best analogy to relativistic quantum field theory is the concept of quasi-particles like phonons, excitons, plasmons and the like which emerge in solid state physics. … Shankar's book goes much deeper than this simple analogy. It examines topics like Majorana fermions, gauge theory, the renormalization group equation, bosonization and triviality. These topics are well known to anybody familiar with the relativistic version of quantum field theory. They … [also] play a role … in condensed matter physics, as the author skillfully explains, touching hereby standard themes of solid state physics like superconductivity, the Ising and Hubbard model and the Hall effect … Every chapter is accompanied by a brief introduction … This is interlaced with remarks on personal experiences of the author. … [the] personal style … is a pedagogical highlight. … The book is perfect …'

Marek Nowakowski Source: Mathematical Reviews

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