Quantum Field Theory and Condensed Matter: An Introduction (Cambridge Monographs on Mathematical Physics)
Cambridge University Press, 8/31/2017
EAN 9780521592109, ISBN10: 0521592100
Hardcover, 450 pages, 25.4 x 18 x 2.3 cm
Language: English
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.