Quantum Field Theory and Condensed Matter
An Introduction

This book provides a review of the application of quantum field theory to condensed matter systems, introducing important techniques in condensed matter theory.

Ramamurti Shankar (Author)

9780521592109, Cambridge University Press

Hardback, published 31 August 2017

450 pages, 56 b/w illus. 3 tables 66 exercises
25.4 x 18.1 x 2.4 cm, 1.05 kg

'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, Mathematical Reviews

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.

Preface
1. Thermodynamics and statistical mechanics review
2. Ising model in d = 0 and d = 1
3. Statistical to quantum mechanics
4. Quantum to statistical mechanics
5. Feynman path integral
6. Coherent state path integrals for spins, bosons and fermions
7. The two-dimensional Ising model
8. Exact solution of the two-dimensional Ising model
9. Majorana fermions
10. Gauge theories
11. The renormalization group
12. Critical phenomena: the puzzle and resolution
13. RG for the ?4 model
14. Two views of renormalization
15. RG for non-relativistic fermions: I
16. RG for non-relativistic fermions: II
17. Bosonization I: the fermion-boson dictionary
18. Bosonization II: selected applications
19. Duality and triality
20. Techniques for the QHE
Index.

Subject Areas: Mathematical physics [PHU], Condensed matter physics [liquid state & solid state physics PHFC]