Quantum Field Theory and Condensed Matter An Introduction

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 ϕ4 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.

Ramamurti Shankar is the John Randolph Huffman Professor of Physics at Yale University, Connecticut, with a research focus in theoretical condensed matter physics. He has held positions at the Aspen Center for Physics, the American Physical Society and the American Academy of Arts and Sciences. He has also been a Visiting Professor at several universities including Massachusetts Institute of Technology, Princeton University, New Jersey, University of California, Berkeley and Indian Institute of Technology, Madras. Recipient of both the Harwood Byrnes and Richard Sewell Teaching Prize at Yale University (2005) and the Julius Edgar Lilienfeld Prize of the American Physical Society (2009), he has also authored several books: Principles of Quantum Mechanics (1994), Basic Training in Mathematics (2008), and Fundamentals of Physics Volume I and Volume II (2014 and 2016).